{"id":2874,"date":"2026-10-28T11:33:03","date_gmt":"2026-10-28T04:33:03","guid":{"rendered":"https:\/\/navi.edu.vn\/blog\/?p=2874"},"modified":"2026-10-28T11:33:03","modified_gmt":"2026-10-28T04:33:03","slug":"de-cuong-on-tap-giua-ki-1-toan-7","status":"publish","type":"post","link":"https:\/\/navi.edu.vn\/blog\/de-cuong-on-tap-giua-ki-1-toan-7\/","title":{"rendered":"\u0110\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7 (2026-2027) &#038; \u0110\u1ec1 thi m\u1eabu c\u00f3 \u0111\u00e1p \u00e1n"},"content":{"rendered":"<div class=\"naviedu-intro-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p>B\u01b0\u1edbc v\u00e0o l\u1edbp 7, h\u1ecdc sinh m\u1edf r\u1ed9ng t\u1eadp s\u1ed1 sang s\u1ed1 h\u1eefu t\u1ec9, s\u1ed1 th\u1ef1c v\u00e0 b\u1eaft \u0111\u1ea7u ti\u1ebfp c\u1eadn b\u1ed9 m\u00f4n h\u00ecnh h\u1ecdc c\u00f3 ch\u1ee9ng minh \u0111\u1ea7y th\u1eed th\u00e1ch.<\/p>\n<p>X\u00e2y d\u1ef1ng m\u1ed9t b\u1ea3n <strong>\u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 to\u00e1n 7<\/strong> chu\u1ea9n x\u00e1c l\u00e0 ch\u00eca kh\u00f3a gi\u00fap c\u00e1c em kh\u1eafc ph\u1ee5c nh\u1eefng n\u1ed7i \u0111au th\u01b0\u1eddng g\u1eb7p nh\u01b0 nh\u1ea7m d\u1ea5u khi t\u00ednh to\u00e1n v\u1edbi s\u1ed1 h\u1eefu t\u1ec9, l\u0169y th\u1eeba, gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i hay l\u00fang t\u00fang khi vi\u1ebft c\u00e1c b\u01b0\u1edbc l\u1eadp lu\u1eadn h\u00ecnh h\u1ecdc. N\u1ebfu kh\u00f4ng th\u00e1o g\u1ee1 k\u1ecbp th\u1eddi, \u0111i\u1ec1u n\u00e0y s\u1ebd d\u1eabn \u0111\u1ebfn vi\u1ec7c <a style=\"color: #0056b3; font-weight: bold; text-decoration: underline;\" href=\"https:\/\/navi.edu.vn\/blog\/con-hoc-toan-khong-tien-bo-7-nguyen-nhan\/\">con h\u1ecdc To\u00e1n kh\u00f4ng ti\u1ebfn b\u1ed9<\/a>.<\/p>\n<p>Hi\u1ec3u \u0111\u01b0\u1ee3c nh\u1eefng tr\u0103n tr\u1edf \u0111\u00f3, NaviEdu g\u1eedi t\u1eb7ng tr\u1ecdn b\u1ed9 t\u00e0i li\u1ec7u to\u00e0n di\u1ec7n g\u1ed3m h\u1ec7 th\u1ed1ng l\u00fd thuy\u1ebft tr\u1ecdng t\u00e2m, ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i chi ti\u1ebft c\u00e1c d\u1ea1ng b\u00e0i th\u01b0\u1eddng g\u1eb7p, l\u1ecbch \u00f4n t\u1eadp khoa h\u1ecdc v\u00e0 \u0111\u1ec1 m\u1eabu c\u00f3 \u0111\u00e1p \u00e1n gi\u00fap h\u1ecdc sinh t\u1ef1 tin b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1.<\/p>\n<\/div>\n<figure style=\"margin: 24px 0; text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2875\" style=\"max-width: 100%; height: auto; border-radius: 10px;\" src=\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-7-tom-tat.png\" alt=\"\u0110\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7 \u2013 t\u00f3m t\u1eaft ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m\" width=\"1200\" height=\"760\" srcset=\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-7-tom-tat.png 1200w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-7-tom-tat-300x190.png 300w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-7-tom-tat-1024x649.png 1024w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-7-tom-tat-768x486.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><figcaption style=\"font-size: 14px; color: #718096; margin-top: 8px;\">S\u01a1 \u0111\u1ed3 t\u00f3m t\u1eaft \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7 (2026\u20132027)<\/figcaption><\/figure>\n<div class=\"naviedu-toc\" style=\"background: #f7fafc; border: 1px solid #e2e8f0; border-radius: 8px; padding: 16px 22px; margin: 24px 0;\">\n<p style=\"margin: 0 0 8px 0; font-weight: bold; color: #0056b3; font-size: 17px;\">M\u1ee5c l\u1ee5c \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7<\/p>\n<ul style=\"margin: 0; padding-left: 22px; line-height: 1.9;\">\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-1-cau-truc-de-thi-giua-ki-1-toan-7-theo-thong-tu-22\">C\u1ea5u tr\u00fac \u0111\u1ec1 thi gi\u1eefa k\u00ec 1 To\u00e1n 7 theo Th\u00f4ng t\u01b0 22<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-2-phan-i-so-huu-ti-va-so-thuc\">Ph\u1ea7n I: S\u1ed1 H\u1eefu T\u1ec9 v\u00e0 S\u1ed1 Th\u1ef1c<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-3-so-huu-ti\">S\u1ed1 h\u1eefu t\u1ec9<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-4-cong-tru-nhan-chia-so-huu-ti\">C\u1ed9ng, tr\u1eeb, nh\u00e2n, chia s\u1ed1 h\u1eefu t\u1ec9<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-5-luy-thua-cua-mot-so-huu-ti\">L\u0169y th\u1eeba c\u1ee7a m\u1ed9t s\u1ed1 h\u1eefu t\u1ec9<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-6-quy-tac-dau-ngoac-va-quy-tac-chuyen-ve\">Quy t\u1eafc d\u1ea5u ngo\u1eb7c v\u00e0 quy t\u1eafc chuy\u1ec3n v\u1ebf<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-7-bieu-dien-thap-phan-cua-so-huu-ti\">Bi\u1ec3u di\u1ec5n th\u1eadp ph\u00e2n c\u1ee7a s\u1ed1 h\u1eefu t\u1ec9<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-8-so-vo-ti-can-bac-hai-so-hoc\">S\u1ed1 v\u00f4 t\u1ec9, c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-9-so-thuc-gia-tri-tuyet-doi\">S\u1ed1 th\u1ef1c, gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-10-phan-ii-goc-va-duong-thang-song-song\">Ph\u1ea7n II: G\u00f3c v\u00e0 \u0110\u01b0\u1eddng Th\u1eb3ng Song Song<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-11-goc-o-vi-tri-dac-biet-tia-phan-giac\">G\u00f3c \u1edf v\u1ecb tr\u00ed \u0111\u1eb7c bi\u1ec7t, tia ph\u00e2n gi\u00e1c<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-12-hai-duong-thang-song-song-tien-de-euclid\">Hai \u0111\u01b0\u1eddng th\u1eb3ng song song, ti\u00ean \u0111\u1ec1 Euclid<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-13-dinh-li-va-chung-minh-dinh-li\">\u0110\u1ecbnh l\u00ed v\u00e0 ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-14-phan-iii-hinh-hoc-truc-quan-hinh-khoi\">Ph\u1ea7n III: H\u00ecnh H\u1ecdc Tr\u1ef1c Quan \u2013 H\u00ecnh Kh\u1ed1i<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-15-hinh-hop-chu-nhat-hinh-lap-phuong\">H\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt, h\u00ecnh l\u1eadp ph\u01b0\u01a1ng<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-16-lang-tru-dung-tam-giac-lang-tru-dung-tu-giac\">L\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c, l\u0103ng tr\u1ee5 \u0111\u1ee9ng t\u1ee9 gi\u00e1c<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-17-phan-iv-lich-on-tap-7-ngay-de-thi-mau\">Ph\u1ea7n IV: L\u1ecbch \u00d4n T\u1eadp 7 Ng\u00e0y &amp; \u0110\u1ec1 Thi M\u1eabu<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-18-lich-on-tap-giua-ki-1-toan-7-trong-7-ngay-giup-con-tu-tin-da\">L\u1ecbch \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7 trong 7 ng\u00e0y gi\u00fap con t\u1ef1 tin \u0111\u1ea1t \u0111i\u1ec3m cao<\/a><\/li>\n<li style=\"font-weight: normal; margin-left: 14px; list-style-type: circle;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-19-tai-de-cuong-on-tap-giua-ki-1-toan-7-va-de-thi-mau-pdf-co-da\">T\u1ea3i \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7 v\u00e0 \u0111\u1ec1 thi m\u1eabu (PDF c\u00f3 \u0111\u00e1p \u00e1n)<\/a><\/li>\n<li style=\"font-weight: bold; list-style-type: disc;\"><a style=\"color: #2d3748; text-decoration: none;\" href=\"#muc-20-loi-ket\">L\u1eddi k\u1ebft<\/a><\/li>\n<\/ul>\n<\/div>\n<p><!-- B\u1eaeT \u0110\u1ea6U: C\u1ea4U TR\u00daC \u0110\u1ec0 THI GI\u1eeeA K\u00cc 1 TO\u00c1N 7 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<h2 id=\"muc-1-cau-truc-de-thi-giua-ki-1-toan-7-theo-thong-tu-22\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 30px; font-size: 22px;\">C\u1ea5u tr\u00fac \u0111\u1ec1 thi gi\u1eefa k\u00ec 1 To\u00e1n 7 theo Th\u00f4ng t\u01b0 22<\/h2>\n<figure id=\"attachment_2898\" aria-describedby=\"caption-attachment-2898\" style=\"width: 800px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2898 size-full\" src=\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-7.png\" alt=\"T\u00ecm hi\u1ec3u v\u1ec1 c\u1ea5u tr\u00fac ma tr\u1eadn \u0111\u1ec1 thi gi\u1eefa k\u1ef3 1 To\u00e1n 7\" width=\"800\" height=\"500\" srcset=\"https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-7.png 800w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-7-300x188.png 300w, https:\/\/navi.edu.vn\/blog\/wp-content\/uploads\/2026\/10\/de-cuong-on-tap-giua-ki-1-toan-7-768x480.png 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><figcaption id=\"caption-attachment-2898\" class=\"wp-caption-text\">T\u00ecm hi\u1ec3u v\u1ec1 c\u1ea5u tr\u00fac ma tr\u1eadn \u0111\u1ec1 thi gi\u1eefa k\u1ef3 1 To\u00e1n 7<\/figcaption><\/figure>\n<p>H\u1ecdc sinh c\u1ea5p THCS \u0111\u01b0\u1ee3c \u0111\u00e1nh gi\u00e1 k\u1ebft qu\u1ea3 h\u1ecdc t\u1eadp theo <a href=\"https:\/\/luatvietnam.vn\/giao-duc\/thong-tu-22-2021-tt-bgddt-207846-d1.html\" target=\"_blank\" rel=\"noopener\">Th\u00f4ng t\u01b0 22\/2021\/TT-BGD\u0110T<\/a>. B\u00e0i ki\u1ec3m tra \u0111\u1ecbnh k\u00ec gi\u1eefa h\u1ecdc k\u00ec 1 m\u00f4n To\u00e1n l\u1edbp 7 th\u01b0\u1eddng c\u00f3 th\u1eddi gian l\u00e0m b\u00e0i l\u00e0 <strong>90 ph\u00fat<\/strong>. V\u00ec ma tr\u1eadn, b\u1ea3n \u0111\u1eb7c t\u1ea3 v\u00e0 \u0111\u1ec1 ki\u1ec3m tra ch\u00ednh th\u1ee9c do t\u1ed5 chuy\u00ean m\u00f4n c\u1ee7a t\u1eebng tr\u01b0\u1eddng THCS t\u1ef1 x\u00e2y d\u1ef1ng (\u0111\u1eb7c bi\u1ec7t hi\u1ec7n nay m\u1ed9t s\u1ed1 tr\u01b0\u1eddng \u0111\u00e3 b\u1eaft \u0111\u1ea7u \u00e1p d\u1ee5ng \u0111\u1ecbnh d\u1ea1ng m\u1edbi b\u1ed5 sung c\u00e1c c\u00e2u h\u1ecfi \u0111\u00fang\/sai v\u00e0 tr\u1ea3 l\u1eddi ng\u1eafn), c\u1ea5u tr\u00fac d\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1eabu tham kh\u1ea3o ph\u1ed5 bi\u1ebfn nh\u1ea5t:<\/p>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Ph\u1ea7n Tr\u1eafc nghi\u1ec7m (Kho\u1ea3ng 3,0 \u2013 4,0 \u0111i\u1ec3m, chi\u1ebfm 30% &#8211; 40% t\u1ed5ng s\u1ed1 \u0111i\u1ec3m):<\/strong> G\u1ed3m c\u00e1c c\u00e2u h\u1ecfi kh\u00e1ch quan nhi\u1ec1u l\u1ef1a ch\u1ecdn (ho\u1eb7c k\u1ebft h\u1ee3p \u0111\u00fang\/sai), ki\u1ec3m tra nhanh kh\u1ea3 n\u0103ng n\u1eafm b\u1eaft l\u00fd thuy\u1ebft c\u01a1 b\u1ea3n v\u1ec1 s\u1ed1 h\u1eefu t\u1ec9, l\u0169y th\u1eeba, g\u00f3c, \u0111\u01b0\u1eddng th\u1eb3ng song song v\u00e0 c\u00e1c h\u00ecnh kh\u1ed1i kh\u00f4ng gian.<\/li>\n<li><strong>Ph\u1ea7n T\u1ef1 lu\u1eadn (Kho\u1ea3ng 6,0 \u2013 7,0 \u0111i\u1ec3m, chi\u1ebfm 60% &#8211; 70% t\u1ed5ng s\u1ed1 \u0111i\u1ec3m):<\/strong> G\u1ed3m c\u00e1c b\u00e0i to\u00e1n th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh, t\u00ecm x (\u00e1p d\u1ee5ng quy t\u1eafc chuy\u1ec3n v\u1ebf, d\u1ea5u ngo\u1eb7c), gi\u1ea3i b\u00e0i to\u00e1n c\u00f3 l\u1eddi v\u0103n t\u1ec9 l\u1ec7 th\u1ee9c, t\u00ednh s\u1ed1 \u0111o g\u00f3c, ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed v\u00e0 t\u00ednh to\u00e1n th\u1ec3 t\u00edch, di\u1ec7n t\u00edch h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt, l\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c.<\/li>\n<\/ul>\n<h3 style=\"color: #2b6cb0; font-size: 18px; margin-top: 22px;\">B\u1ea3ng ma tr\u1eadn tham kh\u1ea3o ph\u00e2n b\u1ed5 n\u1ed9i dung v\u00e0 m\u1ee9c \u0111\u1ed9 nh\u1eadn th\u1ee9c<\/h3>\n<div style=\"overflow-x: auto; margin: 15px 0;\">\n<table style=\"min-width: 640px; table-layout: fixed; font-size: 15px; width: 100%; border-collapse: collapse; border: 1px solid #cbd5e0; text-align: left;\">\n<colgroup>\n<col style=\"width: 22%;\" \/>\n<col style=\"width: 17%;\" \/>\n<col style=\"width: 17%;\" \/>\n<col style=\"width: 17%;\" \/>\n<col style=\"width: 15%;\" \/>\n<col style=\"width: 12%;\" \/><\/colgroup>\n<thead style=\"background-color: #edf2f7;\">\n<tr>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3;\">M\u1ea1ch ki\u1ebfn th\u1ee9c<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">Nh\u1eadn bi\u1ebft<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">Th\u00f4ng hi\u1ec3u<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">V\u1eadn d\u1ee5ng<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">V\u1eadn d\u1ee5ng cao<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; text-align: center;\">T\u1ed5ng \u0111i\u1ec3m<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">S\u1ed1 h\u1eefu t\u1ec9 v\u00e0 c\u00e1c ph\u00e9p t\u00ednh<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; font-weight: bold;\">3,5 \u0111i\u1ec3m<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">S\u1ed1 th\u1ef1c, c\u0103n b\u1eadc hai, gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,75 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,75 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; font-weight: bold;\">2,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">G\u00f3c, \u0111\u01b0\u1eddng th\u1eb3ng song song, \u0111\u1ecbnh l\u00ed<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,75 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,75 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; font-weight: bold;\">3,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">H\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt, l\u1eadp ph\u01b0\u01a1ng, l\u0103ng tr\u1ee5 \u0111\u1ee9ng<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,75 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,5 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0,25 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">0 \u0111i\u1ec3m<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; font-weight: bold;\">1,5 \u0111i\u1ec3m<\/td>\n<\/tr>\n<tr style=\"background-color: #f7fafc; font-weight: bold;\">\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3;\">T\u1ed4NG \u0110I\u1ec2M (T\u1ec8 L\u1ec6 %)<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">4,0 \u0111i\u1ec3m (40%)<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">3,0 \u0111i\u1ec3m (30%)<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">2,0 \u0111i\u1ec3m (20%)<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center;\">1,0 \u0111i\u1ec3m (10%)<\/td>\n<td style=\"white-space: nowrap; word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; text-align: center; color: #c53030;\">10,0 \u0111i\u1ec3m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><!-- H\u1ed8P L\u01afU \u00dd --><\/p>\n<div style=\"background-color: #edf2f7; border-left: 4px solid #0056b3; padding: 14px 18px; border-radius: 4px; margin-top: 25px;\">\n<p style=\"margin: 0; font-size: 15px; color: #2d3748;\"><strong>\ud83d\udca1 L\u01b0u \u00fd quan tr\u1ecdng cho ph\u1ee5 huynh v\u00e0 h\u1ecdc sinh:<\/strong> Ph\u1ea1m vi ki\u1ebfn th\u1ee9c v\u00e0 ph\u00e2n b\u1ed5 \u0111i\u1ec3m s\u1ed1 gi\u1eefa k\u00ec c\u00f3 th\u1ec3 c\u00f3 s\u1ef1 kh\u00e1c bi\u1ec7t nh\u1ecf t\u00f9y theo b\u1ed9 s\u00e1ch gi\u00e1o khoa (K\u1ebft n\u1ed1i tri th\u1ee9c, Ch\u00e2n tr\u1eddi s\u00e1ng t\u1ea1o ho\u1eb7c C\u00e1nh di\u1ec1u) v\u00e0 ti\u1ebfn \u0111\u1ed9 gi\u1ea3ng d\u1ea1y th\u1ef1c t\u1ebf c\u1ee7a t\u1eebng tr\u01b0\u1eddng THCS (v\u00ed d\u1ee5: m\u1ed9t s\u1ed1 tr\u01b0\u1eddng c\u00f3 th\u1ec3 ch\u01b0a \u0111\u01b0a ph\u1ea7n h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c v\u00e0o \u0111\u1ec1 ki\u1ec3m tra gi\u1eefa k\u00ec).<\/p>\n<p style=\"margin: 0; font-size: 15px; color: #2d3748;\">Do \u0111\u00f3, ba m\u1eb9 n\u00ean tham kh\u1ea3o k\u1ef9 \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp do gi\u00e1o vi\u00ean b\u1ed9 m\u00f4n t\u1ea1i tr\u01b0\u1eddng ph\u00e1t ra \u0111\u1ec3 con \u00f4n thi \u0111\u00fang tr\u1ecdng t\u00e2m.<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: C\u1ea4U TR\u00daC \u0110\u1ec0 THI GI\u1eeeA K\u00cc 1 TO\u00c1N 7 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U: PH\u1ea6N I - S\u1ed0 H\u1eeeU T\u1ec8 V\u00c0 S\u1ed0 TH\u1ef0C TO\u00c1N 7 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- BANNER PH\u1ea6N I --><\/p>\n<div style=\"background: linear-gradient(135deg, #0056b3, #0080ff); color: #ffffff; padding: 18px 24px; border-radius: 8px; margin-top: 35px; margin-bottom: 30px;\">\n<h2 id=\"muc-2-phan-i-so-huu-ti-va-so-thuc\" style=\"color: #ffffff; margin: 0; font-size: 22px; text-transform: uppercase; letter-spacing: 0.5px;\">Ph\u1ea7n I: S\u1ed1 H\u1eefu T\u1ec9 v\u00e0 S\u1ed1 Th\u1ef1c<\/h2>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 1: S\u1ed0 H\u1eeeU T\u1ec8 --><\/p>\n<p style=\"margin: 0 0 16px 0;\">S\u1ed1 h\u1eefu t\u1ec9 v\u00e0 c\u00e1c ph\u00e9p t\u00ednh l\u00e0 ph\u1ea7n chi\u1ebfm nhi\u1ec1u \u0111i\u1ec3m nh\u1ea5t trong <strong>\u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7<\/strong>. Con c\u1ea7n th\u1eadt ch\u1eafc quy t\u1eafc d\u1ea5u, v\u00ec ph\u1ea7n l\u1edbn l\u1ed7i m\u1ea5t \u0111i\u1ec3m \u1edf l\u1edbp 7 \u0111\u1ebfn t\u1eeb vi\u1ec7c nh\u1ea7m d\u1ea5u khi t\u00ednh to\u00e1n.<\/p>\n<h2 id=\"muc-3-so-huu-ti\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">S\u1ed1 h\u1eefu t\u1ec9<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">Kh\u00e1i ni\u1ec7m, bi\u1ec3u di\u1ec5n v\u00e0 so s\u00e1nh s\u1ed1 h\u1eefu t\u1ec9<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>\u0110\u1ecbnh ngh\u0129a:<\/strong> S\u1ed1 h\u1eefu t\u1ec9 l\u00e0 s\u1ed1 vi\u1ebft \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 a \/ b, trong \u0111\u00f3 a v\u00e0 b thu\u1ed9c t\u1eadp s\u1ed1 nguy\u00ean Z, v\u00e0 b kh\u00e1c 0. T\u1eadp h\u1ee3p c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 Q.<\/li>\n<li><strong>Bi\u1ec3u di\u1ec5n tr\u00ean tr\u1ee5c s\u1ed1:<\/strong> M\u1ed7i s\u1ed1 h\u1eefu t\u1ec9 \u0111\u1ec1u \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1edfi m\u1ed9t \u0111i\u1ec3m x\u00e1c \u0111\u1ecbnh tr\u00ean tr\u1ee5c s\u1ed1. C\u00e1c s\u1ed1 h\u1eefu t\u1ec9 \u00e2m n\u1eb1m b\u00ean tr\u00e1i \u0111i\u1ec3m 0, c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 d\u01b0\u01a1ng n\u1eb1m b\u00ean ph\u1ea3i \u0111i\u1ec3m 0.<\/li>\n<li><strong>S\u1ed1 \u0111\u1ed1i:<\/strong> M\u1ed7i s\u1ed1 h\u1eefu t\u1ec9 \u0111\u1ec1u c\u00f3 m\u1ed9t s\u1ed1 \u0111\u1ed1i. S\u1ed1 \u0111\u1ed1i c\u1ee7a s\u1ed1 h\u1eefu t\u1ec9 x \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 -x.<\/li>\n<li><strong>So s\u00e1nh hai s\u1ed1 h\u1eefu t\u1ec9:<\/strong> \u0110\u1ec3 so s\u00e1nh hai s\u1ed1 h\u1eefu t\u1ec9, ta c\u00f3 th\u1ec3 vi\u1ebft ch\u00fang d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu d\u01b0\u01a1ng r\u1ed3i so s\u00e1nh c\u00e1c t\u1eed s\u1ed1, ho\u1eb7c \u0111\u01b0a v\u1ec1 d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n \u0111\u1ec3 so s\u00e1nh.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi so s\u00e1nh s\u1ed1 h\u1eefu t\u1ec9 \u00e2m:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>H\u1ecdc sinh th\u01b0\u1eddng qu\u00ean m\u1ea5t t\u00ednh ch\u1ea5t c\u1ee7a s\u1ed1 \u00e2m, nh\u1ea7m l\u1eabn r\u1eb1ng s\u1ed1 n\u00e0o c\u00f3 ph\u1ea7n s\u1ed1 l\u1edbn h\u01a1n th\u00ec l\u1edbn h\u01a1n (v\u00ed d\u1ee5: so s\u00e1nh -3\/4 v\u00e0 -2\/3, n\u1ebfu quy \u0111\u1ed3ng m\u1eabu s\u1ed1 chung l\u00e0 12 ta c\u00f3 -9\/12 v\u00e0 -8\/12, v\u00ec -9 nh\u1ecf h\u01a1n -8 n\u00ean -3\/4 nh\u1ecf h\u01a1n -2\/3).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: So s\u00e1nh hai s\u1ed1 h\u1eefu t\u1ec9<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> So s\u00e1nh hai s\u1ed1 h\u1eefu t\u1ec9 x = -5 \/ 6 v\u00e0 y = -7 \/ 8.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 \u0110\u01b0a hai ph\u00e2n s\u1ed1 v\u1ec1 m\u1eabu s\u1ed1 d\u01b0\u01a1ng chung l\u00e0 24:<br \/>\n&#8211; Ph\u00e2n s\u1ed1 x = (-5 \u00b7 4) \/ (6 \u00b7 4) = -20 \/ 24.<br \/>\n&#8211; Ph\u00e2n s\u1ed1 y = (-7 \u00b7 3) \/ (8 \u00b7 3) = -21 \/ 24.<br \/>\n\u2022 V\u00ec -20 l\u1edbn h\u01a1n -21 n\u00ean -20 \/ 24 l\u1edbn h\u01a1n -21 \/ 24.<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>x l\u1edbn h\u01a1n y (t\u1ee9c -5\/6 l\u1edbn h\u01a1n -7\/8)<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 2: C\u1ed8NG, TR\u1eea, NH\u00c2N, CHIA S\u1ed0 H\u1eeeU T\u1ec8 --><\/p>\n<h2 id=\"muc-4-cong-tru-nhan-chia-so-huu-ti\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">C\u1ed9ng, tr\u1eeb, nh\u00e2n, chia s\u1ed1 h\u1eefu t\u1ec9<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">Quy t\u1eafc t\u00ednh to\u00e1n v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a ph\u00e9p to\u00e1n<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Quy t\u1eafc c\u1ed9ng v\u00e0 tr\u1eeb:<\/strong> Vi\u1ebft c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 c\u00f9ng m\u1eabu s\u1ed1, r\u1ed3i c\u1ed9ng ho\u1eb7c tr\u1eeb c\u00e1c t\u1eed s\u1ed1 v\u1edbi nhau v\u00e0 gi\u1eef nguy\u00ean m\u1eabu s\u1ed1 chung.<\/li>\n<li><strong>Quy t\u1eafc nh\u00e2n v\u00e0 chia:<\/strong> Nh\u00e2n t\u1eed v\u1edbi t\u1eed, m\u1eabu v\u1edbi m\u1eabu \u0111\u1ed1i v\u1edbi ph\u00e9p nh\u00e2n; nh\u00e2n s\u1ed1 b\u1ecb chia v\u1edbi ngh\u1ecbch \u0111\u1ea3o c\u1ee7a s\u1ed1 chia \u0111\u1ed1i v\u1edbi ph\u00e9p chia.<\/li>\n<li><strong>C\u00e1c t\u00ednh ch\u1ea5t c\u1ee7a ph\u00e9p to\u00e1n:<\/strong> Giao ho\u00e1n, k\u1ebft h\u1ee3p v\u00e0 t\u00ednh ch\u1ea5t ph\u00e2n ph\u1ed1i gi\u1eefa ph\u00e9p nh\u00e2n \u0111\u1ed1i v\u1edbi ph\u00e9p c\u1ed9ng gi\u00fap th\u1ef1c hi\u1ec7n t\u00ednh nhanh, t\u00ednh h\u1ee3p l\u00ed.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi t\u00ednh to\u00e1n ph\u00e2n s\u1ed1:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn gi\u1eefa quy t\u1eafc c\u1ed9ng tr\u1eeb (c\u1ea7n quy \u0111\u1ed3ng m\u1eabu s\u1ed1) v\u1edbi quy t\u1eafc nh\u00e2n chia (kh\u00f4ng c\u1ea7n quy \u0111\u1ed3ng m\u1eabu s\u1ed1 m\u00e0 nh\u00e2n th\u1eb3ng t\u1eed v\u1edbi t\u1eed, m\u1eabu v\u1edbi m\u1eabu).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh h\u1ee3p l\u00ed bi\u1ec3u th\u1ee9c s\u1ed1 h\u1eefu t\u1ec9<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c sau m\u1ed9t c\u00e1ch h\u1ee3p l\u00ed: <code>A = (3 \/ 7) \u00b7 (5 \/ 9) + (3 \/ 7) \u00b7 (4 \/ 9) - (3 \/ 7) \u00b7 (2 \/ 9)<\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t ph\u00e2n ph\u1ed1i c\u1ee7a ph\u00e9p nh\u00e2n \u0111\u1ed1i v\u1edbi ph\u00e9p c\u1ed9ng v\u00e0 ph\u00e9p tr\u1eeb:<br \/>\n<code>A = (3 \/ 7) \u00b7 (5 \/ 9 + 4 \/ 9 - 2 \/ 9)<\/code><br \/>\n\u2022 Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh trong ngo\u1eb7c (c\u1ed9ng tr\u1eeb c\u00e1c t\u1eed s\u1ed1 chung m\u1eabu):<\/p>\n<p style=\"margin: 0;\"><code>5 \/ 9 + 4 \/ 9 - 2 \/ 9 = (5 + 4 - 2) \/ 9 = 7 \/ 9<\/code><br \/>\n\u2022 Thay ng\u01b0\u1ee3c l\u1ea1i v\u00e0o bi\u1ec3u th\u1ee9c A:<br \/>\n<code>A = (3 \/ 7) \u00b7 (7 \/ 9) = (3 \u00b7 7) \/ (7 \u00b7 9) = 3 \/ 9 = 1 \/ 3<\/code>.<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>A = 1 \/ 3<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 3: L\u0168Y TH\u1eeaA C\u1ee6A M\u1ed8T S\u1ed0 H\u1eeeU T\u1ec8 --><\/p>\n<h2 id=\"muc-5-luy-thua-cua-mot-so-huu-ti\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">L\u0169y th\u1eeba c\u1ee7a m\u1ed9t s\u1ed1 h\u1eefu t\u1ec9<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">C\u00f4ng th\u1ee9c l\u0169y th\u1eeba v\u00e0 quy t\u1eafc d\u1ea5u<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Kh\u00e1i ni\u1ec7m:<\/strong> L\u0169y th\u1eeba b\u1eadc n c\u1ee7a m\u1ed9t s\u1ed1 h\u1eefu t\u1ec9 x l\u00e0 t\u00edch c\u1ee7a n th\u1eeba s\u1ed1 x (v\u1edbi n l\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean l\u1edbn h\u01a1n 1): <code>x<sup>n<\/sup> = x \u00b7 x \u00b7 ... \u00b7 x<\/code> (n th\u1eeba s\u1ed1). Quy \u01b0\u1edbc: <code>x<sup>1<\/sup> = x<\/code> v\u00e0 <code>x<sup>0<\/sup> = 1<\/code> (v\u1edbi x kh\u00e1c 0).<\/li>\n<li><strong>C\u00e1c c\u00f4ng th\u1ee9c nh\u00e2n chia l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1edf:<\/strong>\n<div style=\"background: #edf2f7; padding: 6px 12px; border-radius: 6px; margin: 6px 0; font-family: monospace; font-weight: bold; color: #2b6cb0;\">x<sup>m<\/sup> \u00b7 x<sup>n<\/sup> = x<sup>m + n<\/sup><br \/>\nx<sup>m<\/sup> : x<sup>n<\/sup> = x<sup>m &#8211; n<\/sup> \u00a0\u00a0(v\u1edbi x kh\u00e1c 0, m l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng n)<br \/>\n(x<sup>m<\/sup>)<sup>n<\/sup> = x<sup>m \u00b7 n<\/sup><\/div>\n<\/li>\n<li><strong>Quy t\u1eafc d\u1ea5u c\u1ee7a l\u0169y th\u1eeba s\u1ed1 \u00e2m:<\/strong> L\u0169y th\u1eeba v\u1edbi s\u1ed1 m\u0169 ch\u1eb5n c\u1ee7a m\u1ed9t s\u1ed1 \u00e2m lu\u00f4n mang k\u1ebft qu\u1ea3 d\u01b0\u01a1ng; l\u0169y th\u1eeba v\u1edbi s\u1ed1 m\u0169 l\u1ebb c\u1ee7a m\u1ed9t s\u1ed1 \u00e2m lu\u00f4n mang k\u1ebft qu\u1ea3 \u00e2m.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 d\u1ea5u l\u0169y th\u1eeba:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn gi\u1eefa bi\u1ec3u th\u1ee9c <code>(-2)<sup>4<\/sup><\/code> (b\u1eb1ng 16 v\u00ec c\u00f3 d\u1ea5u ngo\u1eb7c) v\u1edbi bi\u1ec3u th\u1ee9c <code>-2<sup>4<\/sup><\/code> (b\u1eb1ng -16 v\u00ec d\u1ea5u tr\u1eeb \u0111\u1ee9ng \u0111\u1ed9c l\u1eadp tr\u01b0\u1edbc l\u0169y th\u1eeba).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: R\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c l\u0169y th\u1eeba<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c: <code>B = (2<sup>5<\/sup> \u00b7 2<sup>3<\/sup>) \/ 2<sup>4<\/sup><\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 \u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c nh\u00e2n hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1edf \u1edf t\u1eed s\u1ed1:<br \/>\n<code>2<sup>5<\/sup> \u00b7 2<sup>3<\/sup> = 2<sup>5 + 3<\/sup> = 2<sup>8<\/sup><\/code>.<br \/>\n\u2022 \u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c chia hai l\u0169y th\u1eeba c\u00f9ng c\u01a1 s\u1edf:<br \/>\n<code>B = 2<sup>8<\/sup> \/ 2<sup>4<\/sup> = 2<sup>8 - 4<\/sup> = 2<sup>4<\/sup><\/code>.<br \/>\n\u2022 T\u00ednh gi\u00e1 tr\u1ecb l\u0169y th\u1eeba: <code>2<sup>4<\/sup> = 16<\/code>.<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>B = 16<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 4: QUY T\u1eaeC D\u1ea4U NGO\u1eb6C V\u00c0 QUY T\u1eaeC CHUY\u1ec2N V\u1ebe --><\/p>\n<h2 id=\"muc-6-quy-tac-dau-ngoac-va-quy-tac-chuyen-ve\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">Quy t\u1eafc d\u1ea5u ngo\u1eb7c v\u00e0 quy t\u1eafc chuy\u1ec3n v\u1ebf<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">Ph\u01b0\u01a1ng ph\u00e1p b\u1ecf ngo\u1eb7c, chuy\u1ec3n v\u1ebf v\u00e0 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh t\u00ecm x<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Quy t\u1eafc d\u1ea5u ngo\u1eb7c:<\/strong>\n<ul>\n<li>Khi b\u1ecf d\u1ea5u ngo\u1eb7c c\u00f3 d\u1ea5u c\u1ed9ng &#8220;+&#8221; \u0111\u1eb1ng tr\u01b0\u1edbc, ta gi\u1eef nguy\u00ean d\u1ea5u c\u1ee7a c\u00e1c s\u1ed1 h\u1ea1ng b\u00ean trong.<\/li>\n<li>Khi b\u1ecf d\u1ea5u ngo\u1eb7c c\u00f3 d\u1ea5u tr\u1eeb &#8220;-&#8221; \u0111\u1eb1ng tr\u01b0\u1edbc, ta ph\u1ea3i \u0111\u1ed5i d\u1ea5u to\u00e0n b\u1ed9 c\u00e1c s\u1ed1 h\u1ea1ng b\u00ean trong (d\u1ea5u c\u1ed9ng th\u00e0nh tr\u1eeb, d\u1ea5u tr\u1eeb th\u00e0nh c\u1ed9ng).<\/li>\n<\/ul>\n<\/li>\n<li><strong>Quy t\u1eafc chuy\u1ec3n v\u1ebf:<\/strong> Khi chuy\u1ec3n m\u1ed9t s\u1ed1 h\u1ea1ng t\u1eeb v\u1ebf n\u00e0y sang v\u1ebf kia c\u1ee7a m\u1ed9t \u0111\u1eb3ng th\u1ee9c, ta ph\u1ea3i \u0111\u1ed5i d\u1ea5u s\u1ed1 h\u1ea1ng \u0111\u00f3 (d\u1ea5u c\u1ed9ng \u0111\u1ed5i th\u00e0nh d\u1ea5u tr\u1eeb v\u00e0 ng\u01b0\u1ee3c l\u1ea1i).<\/li>\n<li><strong>D\u1ea1ng to\u00e1n t\u00ecm x:<\/strong> S\u1eed d\u1ee5ng k\u1ebft h\u1ee3p quy t\u1eafc chuy\u1ec3n v\u1ebf, quy t\u1eafc d\u1ea5u ngo\u1eb7c v\u00e0 c\u00e1c ph\u00e9p t\u00ednh s\u1ed1 h\u1eefu t\u1ec9 \u0111\u1ec3 c\u00f4 l\u1eadp \u1ea9n x v\u00e0 t\u00ecm gi\u00e1 tr\u1ecb ch\u00ednh x\u00e1c.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi gi\u1ea3i to\u00e1n t\u00ecm x:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean \u0111\u1ed5i d\u1ea5u c\u00e1c s\u1ed1 h\u1ea1ng b\u00ean trong ngo\u1eb7c khi ph\u00e1 ngo\u1eb7c c\u00f3 d\u1ea5u tr\u1eeb \u0111\u1eb1ng tr\u01b0\u1edbc, ho\u1eb7c qu\u00ean \u0111\u1ed5i d\u1ea5u s\u1ed1 h\u1ea1ng khi chuy\u1ec3n v\u1ebf qua d\u1ea5u b\u1eb1ng.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: B\u00e0i to\u00e1n t\u00ecm x c\u01a1 b\u1ea3n<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> T\u00ecm s\u1ed1 h\u1eefu t\u1ec9 x, bi\u1ebft: <code>3 \/ 4 - (x + 1 \/ 2) = 1 \/ 3<\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 Ph\u00e1 d\u1ea5u ngo\u1eb7c c\u00f3 d\u1ea5u tr\u1eeb \u0111\u1eb1ng tr\u01b0\u1edbc (\u0111\u1ed5i d\u1ea5u c\u00e1c s\u1ed1 h\u1ea1ng b\u00ean trong):<br \/>\n<code>3 \/ 4 - x - 1 \/ 2 = 1 \/ 3<\/code>.<br \/>\n\u2022 Chuy\u1ec3n c\u00e1c s\u1ed1 h\u1ea1ng t\u1ef1 do sang v\u1ebf ph\u1ea3i v\u00e0 gi\u1eef \u1ea9n x \u1edf v\u1ebf tr\u00e1i:<br \/>\n<code>-x = 1 \/ 3 - 3 \/ 4 + 1 \/ 2<\/code>.<\/p>\n<p style=\"margin: 0;\">\u2022 Quy \u0111\u1ed3ng m\u1eabu s\u1ed1 chung v\u1ebf ph\u1ea3i l\u00e0 12:<br \/>\n<code>-x = 4 \/ 12 - 9 \/ 12 + 6 \/ 12 = (4 - 9 + 6) \/ 12 = 1 \/ 12<\/code>.<br \/>\n\u2022 Suy ra <code>x = -1 \/ 12<\/code>.<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>x = -1 \/ 12<\/strong>.<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: PH\u1ea6N I - S\u1ed0 H\u1eeeU T\u1ec8 V\u00c0 S\u1ed0 TH\u1ef0C TO\u00c1N 7 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U: PH\u1ea6N I (TI\u1ebeP THEO) - S\u1ed0 TH\u1eacP PH\u00c2N, S\u1ed0 V\u00d4 T\u1ec8 V\u00c0 S\u1ed0 TH\u1ef0C TO\u00c1N 7 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- CH\u1ee6 \u0110\u1ec0 5: BI\u1ec2U DI\u1ec4N TH\u1eacP PH\u00c2N C\u1ee6A S\u1ed0 H\u1eeeU T\u1ec8 --><\/p>\n<p style=\"margin: 0 0 16px 0;\">Ti\u1ebfp theo, \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7 m\u1edf r\u1ed9ng sang s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n, s\u1ed1 v\u00f4 t\u1ec9 v\u00e0 s\u1ed1 th\u1ef1c. \u0110\u00e2y l\u00e0 nh\u00f3m ki\u1ebfn th\u1ee9c m\u1edbi, hay xu\u1ea5t hi\u1ec7n \u1edf c\u00e1c c\u00e2u tr\u1eafc nghi\u1ec7m nh\u1eadn bi\u1ebft.<\/p>\n<h2 id=\"muc-7-bieu-dien-thap-phan-cua-so-huu-ti\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">Bi\u1ec3u di\u1ec5n th\u1eadp ph\u00e2n c\u1ee7a s\u1ed1 h\u1eefu t\u1ec9<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">Ph\u00e2n lo\u1ea1i s\u1ed1 th\u1eadp ph\u00e2n v\u00e0 quy t\u1eafc l\u00e0m tr\u00f2n<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Kh\u00e1i ni\u1ec7m:<\/strong> M\u1ed7i s\u1ed1 h\u1eefu t\u1ec9 \u0111\u1ec1u \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1edfi m\u1ed9t s\u1ed1 th\u1eadp ph\u00e2n h\u1eefu h\u1ea1n ho\u1eb7c s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n tu\u1ea7n ho\u00e0n. V\u00ed d\u1ee5 ph\u00e2n s\u1ed1 1\/3 \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n tu\u1ea7n ho\u00e0n l\u00e0 0,(3).<\/li>\n<li><strong>D\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft ph\u00e2n s\u1ed1 bi\u1ec3u di\u1ec5n \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n h\u1eefu h\u1ea1n:<\/strong> M\u1ed9t ph\u00e2n s\u1ed1 t\u1ed1i gi\u1ea3n v\u1edbi m\u1eabu s\u1ed1 d\u01b0\u01a1ng m\u00e0 m\u1eabu kh\u00f4ng c\u00f3 \u01b0\u1edbc nguy\u00ean t\u1ed1 kh\u00e1c 2 v\u00e0 5 th\u00ec ph\u00e2n s\u1ed1 \u0111\u00f3 bi\u1ec3u di\u1ec5n \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n h\u1eefu h\u1ea1n. Ng\u01b0\u1ee3c l\u1ea1i, n\u1ebfu m\u1eabu ch\u1ee9a \u01b0\u1edbc nguy\u00ean t\u1ed1 kh\u00e1c 2 v\u00e0 5 th\u00ec bi\u1ec3u di\u1ec5n th\u00e0nh s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n tu\u1ea7n ho\u00e0n.<\/li>\n<li><strong>Quy t\u1eafc l\u00e0m tr\u00f2n s\u1ed1 th\u1eadp ph\u00e2n:<\/strong>\n<ul>\n<li>N\u1ebfu ch\u1eef s\u1ed1 b\u1ecf \u0111i nh\u1ecf h\u01a1n 5, ta gi\u1eef nguy\u00ean b\u1ed9 ph\u1eadn c\u00f2n l\u1ea1i (l\u00e0m tr\u00f2n xu\u1ed1ng).<\/li>\n<li>N\u1ebfu ch\u1eef s\u1ed1 b\u1ecf \u0111i l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 5, ta c\u1ed9ng th\u00eam 1 \u0111\u01a1n v\u1ecb v\u00e0o ch\u1eef s\u1ed1 cu\u1ed1i c\u00f9ng c\u1ee7a ph\u1ea7n gi\u1eef l\u1ea1i (l\u00e0m tr\u00f2n l\u00ean).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi l\u00e0m tr\u00f2n s\u1ed1:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean x\u00e9t c\u00e1c ch\u1eef s\u1ed1 ph\u00eda sau ch\u1eef s\u1ed1 l\u00e0m tr\u00f2n (l\u00e0m tr\u00f2n li\u00ean ti\u1ebfp sai) ho\u1eb7c nh\u1ea7m l\u1eabn gi\u1eefa quy t\u1eafc l\u00e0m tr\u00f2n \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 n v\u1edbi l\u00e0m tr\u00f2n theo \u0111\u1ed9 ch\u00ednh x\u00e1c cho tr\u01b0\u1edbc.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Nh\u1eadn bi\u1ebft d\u1ea1ng th\u1eadp ph\u00e2n v\u00e0 l\u00e0m tr\u00f2n s\u1ed1<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong><br \/>\na) Ph\u00e2n s\u1ed1 n\u00e0o sau \u0111\u00e2y bi\u1ec3u di\u1ec5n s\u1ed1 th\u1eadp ph\u00e2n h\u1eefu h\u1ea1n: 3\/8, 5\/12?<br \/>\nb) L\u00e0m tr\u00f2n s\u1ed1 th\u1eadp ph\u00e2n a = 12,3456 \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 X\u00e9t \u00fd a:<br \/>\n&#8211; Ph\u00e2n s\u1ed1 3\/8 c\u00f3 m\u1eabu s\u1ed1 8 = 2<sup>3<\/sup> (ch\u1ec9 c\u00f3 \u01b0\u1edbc nguy\u00ean t\u1ed1 2), do \u0111\u00f3 3\/8 bi\u1ec3u di\u1ec5n \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n h\u1eefu h\u1ea1n.<br \/>\n&#8211; Ph\u00e2n s\u1ed1 5\/12 c\u00f3 m\u1eabu s\u1ed1 12 = 2<sup>2<\/sup> \u00b7 3 (ch\u1ee9a \u01b0\u1edbc nguy\u00ean t\u1ed1 3 kh\u00e1c 2 v\u00e0 5), do \u0111\u00f3 5\/12 bi\u1ec3u di\u1ec5n th\u00e0nh s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n tu\u1ea7n ho\u00e0n.<br \/>\n\u2022 X\u00e9t \u00fd b:<br \/>\n&#8211; L\u00e0m tr\u00f2n s\u1ed1 12,3456 \u0111\u1ebfn ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 hai (ch\u1eef s\u1ed1 4).<\/p>\n<p style=\"margin: 0;\">X\u00e9t ch\u1eef s\u1ed1 ngay sau n\u00f3 l\u00e0 ch\u1eef s\u1ed1 5.<br \/>\n&#8211; V\u00ec ch\u1eef s\u1ed1 sau l\u00e0 5 n\u00ean ta c\u1ed9ng 1 v\u00e0o ch\u1eef s\u1ed1 4, ta \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 l\u00e0m tr\u00f2n l\u00e0 12,35.<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>a) Ph\u00e2n s\u1ed1 3\/8 ; b) 12,35<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 6: S\u1ed0 V\u00d4 T\u1ec8, C\u0102N B\u1eacC HAI S\u1ed0 H\u1eccC --><\/p>\n<h2 id=\"muc-8-so-vo-ti-can-bac-hai-so-hoc\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">S\u1ed1 v\u00f4 t\u1ec9, c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">\u0110\u1ecbnh ngh\u0129a s\u1ed1 v\u00f4 t\u1ec9 v\u00e0 c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>S\u1ed1 v\u00f4 t\u1ec9:<\/strong> L\u00e0 s\u1ed1 vi\u1ebft \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n kh\u00f4ng tu\u1ea7n ho\u00e0n. T\u1eadp h\u1ee3p c\u00e1c s\u1ed1 v\u00f4 t\u1ec9 \u0111\u01b0\u1ee3c k\u00ed hi\u1ec7u l\u00e0 I.<\/li>\n<li><strong>C\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc:<\/strong> C\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc c\u1ee7a m\u1ed9t s\u1ed1 a kh\u00f4ng \u00e2m (k\u00ed hi\u1ec7u l\u00e0 \u221aa) l\u00e0 s\u1ed1 x kh\u00f4ng \u00e2m sao cho x<sup>2<\/sup> = a.<br \/>\n<em>V\u00ed d\u1ee5:<\/em> C\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc c\u1ee7a 25 l\u00e0 <code>\u221a25 = 5<\/code> (l\u01b0u \u00fd k\u1ebft qu\u1ea3 lu\u00f4n mang gi\u00e1 tr\u1ecb kh\u00f4ng \u00e2m, kh\u00f4ng l\u1ea5y gi\u00e1 tr\u1ecb -5).<\/li>\n<li><strong>S\u1eed d\u1ee5ng m\u00e1y t\u00ednh c\u1ea7m tay:<\/strong> C\u00f3 th\u1ec3 d\u00f9ng m\u00e1y t\u00ednh \u0111\u1ec3 t\u00ednh g\u1ea7n \u0111\u00fang gi\u00e1 tr\u1ecb c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc c\u1ee7a c\u00e1c s\u1ed1 kh\u00f4ng ch\u00ednh ph\u01b0\u01a1ng v\u1edbi \u0111\u1ed9 ch\u00ednh x\u00e1c mong mu\u1ed1n.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 c\u0103n b\u1eadc hai:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn k\u00ed hi\u1ec7u c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc v\u1edbi nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh x<sup>2<\/sup> = a (vi\u1ebft sai r\u1eb1ng \u221a25 = \u00b15 thay v\u00ec \u0111\u00fang b\u1ea3n ch\u1ea5t l\u00e0 \u221a25 = 5).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c ch\u1ee9a c\u0103n b\u1eadc hai<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c: <code>C = \u221a(81) - 2 \u00b7 \u221a(16) + 3<\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 T\u00ednh t\u1eebng c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc:<br \/>\n&#8211; <code>\u221a(81) = 9<\/code> (v\u00ec 9<sup>2<\/sup> = 81).<br \/>\n&#8211; <code>\u221a(16) = 4<\/code> (v\u00ec 4<sup>2<\/sup> = 16).<br \/>\n\u2022 Thay c\u00e1c gi\u00e1 tr\u1ecb v\u1eeba t\u00ednh v\u00e0o bi\u1ec3u th\u1ee9c C:<br \/>\n<code>C = 9 - 2 \u00b7 4 + 3<\/code><br \/>\n<code>C = 9 - 8 + 3 = 1 + 3 = 4<\/code>.<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>C = 4<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 7: S\u1ed0 TH\u1ef0C, GI\u00c1 TR\u1eca TUY\u1ec6T \u0110\u1ed0I --><\/p>\n<h2 id=\"muc-9-so-thuc-gia-tri-tuyet-doi\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">S\u1ed1 th\u1ef1c, gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">T\u1eadp h\u1ee3p s\u1ed1 th\u1ef1c v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Kh\u00e1i ni\u1ec7m s\u1ed1 th\u1ef1c:<\/strong> S\u1ed1 h\u1eefu t\u1ec9 v\u00e0 s\u1ed1 v\u00f4 t\u1ec9 chung g\u1ecdi l\u00e0 s\u1ed1 th\u1ef1c. T\u1eadp h\u1ee3p c\u00e1c s\u1ed1 th\u1ef1c \u0111\u01b0\u1ee3c k\u00ed hi\u1ec7u l\u00e0 R (ch\u1ee9a \u0111\u1ea7y \u0111\u1ee7 c\u00e1c t\u1eadp N, Z, Q, I).<\/li>\n<li><strong>Tr\u1ee5c s\u1ed1 th\u1ef1c:<\/strong> M\u1ed7i s\u1ed1 th\u1ef1c \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1edfi m\u1ed9t \u0111i\u1ec3m tr\u00ean tr\u1ee5c s\u1ed1 th\u1ef1c, v\u00e0 ng\u01b0\u1ee3c l\u1ea1i m\u1ed7i \u0111i\u1ec3m tr\u00ean tr\u1ee5c s\u1ed1 th\u1ef1c \u0111\u1ec1u bi\u1ec3u di\u1ec5n m\u1ed9t s\u1ed1 th\u1ef1c.<\/li>\n<li><strong>Gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a m\u1ed9t s\u1ed1 th\u1ef1c x:<\/strong>\n<div style=\"background: #edf2f7; padding: 6px 12px; border-radius: 6px; margin: 6px 0; font-family: monospace; font-weight: bold; color: #2b6cb0;\">|x| = x \u00a0\u00a0(n\u1ebfu x l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0)<br \/>\n|x| = -x \u00a0\u00a0(n\u1ebfu x nh\u1ecf h\u01a1n 0)<\/div>\n<p><em>T\u00ednh ch\u1ea5t:<\/em> Gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a m\u1ecdi s\u1ed1 th\u1ef1c \u0111\u1ec1u l\u00e0 m\u1ed9t s\u1ed1 kh\u00f4ng \u00e2m (|x| l\u1edbn h\u01a1n ho\u1eb7c b\u1eb1ng 0 v\u1edbi m\u1ecdi x).<\/li>\n<li><strong>Ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i:<\/strong>\n<ul>\n<li>N\u1ebfu <code>|x| = a<\/code> (v\u1edbi a &gt; 0) th\u00ec <code>x = a<\/code> ho\u1eb7c <code>x = -a<\/code>.<\/li>\n<li>D\u1ea1ng m\u1edf r\u1ed9ng <code>|x - 1| = 3<\/code> t\u01b0\u01a1ng \u0111\u01b0\u01a1ng <code>x - 1 = 3<\/code> ho\u1eb7c <code>x - 1 = -3<\/code>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean m\u1ea5t tr\u01b0\u1eddng h\u1ee3p \u00e2m khi gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i (ch\u1ec9 t\u00ecm \u0111\u01b0\u1ee3c m\u1ed9t nghi\u1ec7m d\u01b0\u01a1ng m\u00e0 b\u1ecf qu\u00ean nghi\u1ec7m \u00e2m c\u00f2n l\u1ea1i).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 th\u1ef1c x, bi\u1ebft: <code>|2x - 1| = 3<\/code>.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 Theo \u0111\u1ecbnh ngh\u0129a gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i, ph\u01b0\u01a1ng tr\u00ecnh <code>|2x - 1| = 3<\/code> x\u1ea3y ra hai tr\u01b0\u1eddng h\u1ee3p:<br \/>\n&#8211; Tr\u01b0\u1eddng h\u1ee3p 1: <code>2x - 1 = 3<\/code> t\u01b0\u01a1ng \u0111\u01b0\u01a1ng <code>2x = 4<\/code> t\u01b0\u01a1ng \u0111\u01b0\u01a1ng <code>x = 2<\/code>.<br \/>\n&#8211; Tr\u01b0\u1eddng h\u1ee3p 2: <code>2x - 1 = -3<\/code> t\u01b0\u01a1ng \u0111\u01b0\u01a1ng <code>2x = -2<\/code> t\u01b0\u01a1ng \u0111\u01b0\u01a1ng <code>x = -1<\/code>.<br \/>\n\u2022 K\u1ebft lu\u1eadn c\u00e1c gi\u00e1 tr\u1ecb x th\u1ecfa m\u00e3n.<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>x = 2 ho\u1eb7c x = -1<\/strong>.<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: PH\u1ea6N I (TI\u1ebeP THEO) - S\u1ed0 TH\u1eacP PH\u00c2N, S\u1ed0 V\u00d4 T\u1ec8 V\u00c0 S\u1ed0 TH\u1ef0C TO\u00c1N 7 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U: PH\u1ea6N II - G\u00d3C V\u00c0 \u0110\u01af\u1edcNG TH\u1eb2NG SONG SONG TO\u00c1N 7 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- BANNER PH\u1ea6N II --><\/p>\n<div style=\"background: linear-gradient(135deg, #0056b3, #0080ff); color: #ffffff; padding: 18px 24px; border-radius: 8px; margin-top: 35px; margin-bottom: 30px;\">\n<h2 id=\"muc-10-phan-ii-goc-va-duong-thang-song-song\" style=\"color: #ffffff; margin: 0; font-size: 22px; text-transform: uppercase; letter-spacing: 0.5px;\">Ph\u1ea7n II: G\u00f3c v\u00e0 \u0110\u01b0\u1eddng Th\u1eb3ng Song Song<\/h2>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 1: G\u00d3C \u1ede V\u1eca TR\u00cd \u0110\u1eb6C BI\u1ec6T, TIA PH\u00c2N GI\u00c1C --><\/p>\n<p style=\"margin: 0 0 16px 0;\">Ph\u1ea7n h\u00ecnh h\u1ecdc trong \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7 \u0111\u00e1nh d\u1ea5u l\u1ea7n \u0111\u1ea7u con ph\u1ea3i vi\u1ebft l\u1eadp lu\u1eadn ch\u1ee9ng minh. H\u00e3y t\u1eadp ghi r\u00f5 c\u0103n c\u1ee9 cho t\u1eebng b\u01b0\u1edbc ngay t\u1eeb nh\u1eefng b\u00e0i t\u00ednh g\u00f3c \u0111\u01a1n gi\u1ea3n.<\/p>\n<h2 id=\"muc-11-goc-o-vi-tri-dac-biet-tia-phan-giac\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">G\u00f3c \u1edf v\u1ecb tr\u00ed \u0111\u1eb7c bi\u1ec7t, tia ph\u00e2n gi\u00e1c<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">T\u00ednh ch\u1ea5t c\u00e1c g\u00f3c \u0111\u1eb7c bi\u1ec7t v\u00e0 tia ph\u00e2n gi\u00e1c<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>Hai g\u00f3c k\u1ec1 b\u00f9:<\/strong> L\u00e0 hai g\u00f3c v\u1eeba c\u00f3 m\u1ed9t c\u1ea1nh chung, v\u1eeba c\u00f3 hai c\u1ea1nh c\u00f2n l\u1ea1i n\u1eb1m tr\u00ean hai tia \u0111\u1ed1i nhau. T\u1ed5ng s\u1ed1 \u0111o c\u1ee7a hai g\u00f3c k\u1ec1 b\u00f9 lu\u00f4n b\u1eb1ng <code>180\u00b0<\/code>.<\/li>\n<li><strong>Hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh:<\/strong> L\u00e0 hai g\u00f3c m\u00e0 m\u1ed7i c\u1ea1nh c\u1ee7a g\u00f3c n\u00e0y l\u00e0 tia \u0111\u1ed1i c\u1ee7a m\u1ed9t c\u1ea1nh c\u1ee7a g\u00f3c kia. Hai g\u00f3c \u0111\u1ed1i \u0111\u1ec9nh th\u00ec <strong>lu\u00f4n b\u1eb1ng nhau<\/strong>.<\/li>\n<li><strong>Tia ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c:<\/strong> L\u00e0 tia xu\u1ea5t ph\u00e1t t\u1eeb \u0111\u1ec9nh c\u1ee7a g\u00f3c, n\u1eb1m gi\u1eefa hai c\u1ea1nh c\u1ee7a g\u00f3c v\u00e0 chia g\u00f3c \u0111\u00f3 th\u00e0nh hai g\u00f3c c\u00f3 s\u1ed1 \u0111o b\u1eb1ng nhau (t\u1ee9c l\u00e0 b\u1eb1ng m\u1ed9t n\u1eeda s\u1ed1 \u0111o g\u00f3c ban \u0111\u1ea7u).<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 g\u00f3c k\u1ec1 b\u00f9:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn gi\u1eefa g\u00f3c k\u1ec1 b\u00f9 (t\u1ed5ng b\u1eb1ng 180\u00b0) v\u1edbi g\u00f3c ph\u1ee5 nhau (t\u1ed5ng b\u1eb1ng 90\u00b0) ho\u1eb7c ng\u1ed9 nh\u1eadn r\u1eb1ng c\u1ee9 hai g\u00f3c c\u00f3 chung m\u1ed9t c\u1ea1nh l\u00e0 k\u1ec1 b\u00f9.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh s\u1ed1 \u0111o g\u00f3c d\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t k\u1ec1 b\u00f9 v\u00e0 \u0111\u1ed1i \u0111\u1ec9nh<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho g\u00f3c xOy = 60\u00b0, Oz l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c xOy, Ot l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia Oz. T\u00ednh s\u1ed1 \u0111o g\u00f3c k\u1ec1 b\u00f9 v\u1edbi g\u00f3c xOy v\u00e0 s\u1ed1 \u0111o g\u00f3c yOt.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 T\u00ednh s\u1ed1 \u0111o g\u00f3c k\u1ec1 b\u00f9 v\u1edbi g\u00f3c xOy:<br \/>\n&#8211; G\u1ecdi g\u00f3c xOy&#8217; l\u00e0 g\u00f3c k\u1ec1 b\u00f9 v\u1edbi g\u00f3c xOy. Ta c\u00f3:<\/p>\n<p style=\"margin: 0;\"><code>g\u00f3c xOy + g\u00f3c xOy' = 180\u00b0<\/code>.<br \/>\n&#8211; Suy ra g\u00f3c k\u1ec1 b\u00f9 = <code>180\u00b0 - 60\u00b0 = 120\u00b0<\/code>.<br \/>\n\u2022 T\u00ednh s\u1ed1 \u0111o g\u00f3c yOt:<br \/>\n&#8211; V\u00ec Oz l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c xOy n\u00ean <code>g\u00f3c yOz = 60\u00b0 : 2 = 30\u00b0<\/code>.<br \/>\n&#8211; V\u00ec Ot l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia Oz n\u00ean g\u00f3c yOt k\u1ec1 b\u00f9 v\u1edbi g\u00f3c yOz. Do \u0111\u00f3 g\u00f3c yOt = <code>180\u00b0 - 30\u00b0 = 150\u00b0<\/code>.<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>G\u00f3c k\u1ec1 b\u00f9 b\u1eb1ng 120\u00b0 v\u00e0 g\u00f3c yOt b\u1eb1ng 150\u00b0<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 2: HAI \u0110\u01af\u1edcNG TH\u1eb2NG SONG SONG, TI\u00caN \u0110\u1ec0 EUCLID --><\/p>\n<h2 id=\"muc-12-hai-duong-thang-song-song-tien-de-euclid\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">Hai \u0111\u01b0\u1eddng th\u1eb3ng song song, ti\u00ean \u0111\u1ec1 Euclid<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">G\u00f3c t\u1ea1o b\u1edfi m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft hai \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 ti\u00ean \u0111\u1ec1 Euclid<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>C\u00e1c c\u1eb7p g\u00f3c \u0111\u1eb7c bi\u1ec7t:<\/strong> Khi \u0111\u01b0\u1eddng th\u1eb3ng c c\u1eaft hai \u0111\u01b0\u1eddng th\u1eb3ng a v\u00e0 b, ta c\u00f3 c\u00e1c c\u1eb7p g\u00f3c so le trong, g\u00f3c \u0111\u1ed3ng v\u1ecb, v\u00e0 g\u00f3c trong c\u00f9ng ph\u00eda.<\/li>\n<li><strong>D\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft:<\/strong> N\u1ebfu \u0111\u01b0\u1eddng th\u1eb3ng c c\u1eaft hai \u0111\u01b0\u1eddng th\u1eb3ng a, b v\u00e0 trong c\u00e1c g\u00f3c t\u1ea1o th\u00e0nh c\u00f3 m\u1ed9t c\u1eb7p g\u00f3c so le trong b\u1eb1ng nhau (ho\u1eb7c m\u1ed9t c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng nhau, ho\u1eb7c t\u1ed5ng hai g\u00f3c trong c\u00f9ng ph\u00eda b\u1eb1ng 180\u00b0) th\u00ec a v\u00e0 b <strong>song song v\u1edbi nhau<\/strong>.<\/li>\n<li><strong>Ti\u00ean \u0111\u1ec1 Euclid v\u1ec1 \u0111\u01b0\u1eddng th\u1eb3ng song song:<\/strong> Qua m\u1ed9t \u0111i\u1ec3m \u1edf ngo\u00e0i m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng, ch\u1ec9 c\u00f3 \u0111\u00fang m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3.<\/li>\n<li><strong>T\u00ednh ch\u1ea5t hai \u0111\u01b0\u1eddng th\u1eb3ng song song:<\/strong> N\u1ebfu m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft hai \u0111\u01b0\u1eddng th\u1eb3ng song song th\u00ec hai g\u00f3c so le trong b\u1eb1ng nhau, hai g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng nhau, v\u00e0 hai g\u00f3c trong c\u00f9ng ph\u00eda b\u00f9 nhau. M\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1ed9t trong hai \u0111\u01b0\u1eddng th\u1eb3ng song song th\u00ec c\u0169ng vu\u00f4ng g\u00f3c v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng c\u00f2n l\u1ea1i.<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi d\u00f9ng t\u00ednh ch\u1ea5t song song:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn t\u00ednh ch\u1ea5t c\u1ee7a hai g\u00f3c trong c\u00f9ng ph\u00eda (nhi\u1ec1u h\u1ecdc sinh t\u01b0\u1edfng nh\u1ea7m hai g\u00f3c trong c\u00f9ng ph\u00eda b\u1eb1ng nhau thay v\u00ec b\u00f9 nhau c\u00f3 t\u1ed5ng b\u1eb1ng 180\u00b0).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh s\u1ed1 \u0111o g\u00f3c t\u1ea1o b\u1edfi hai \u0111\u01b0\u1eddng th\u1eb3ng song song<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho \u0111\u01b0\u1eddng th\u1eb3ng a song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng b. M\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng a t\u1ea1i \u0111i\u1ec3m A v\u00e0 c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng b t\u1ea1i \u0111i\u1ec3m B sao cho m\u1ed9t g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng <code>70\u00b0<\/code>. T\u00ednh s\u1ed1 \u0111o c\u00e1c g\u00f3c c\u00f2n l\u1ea1i t\u1ea1i \u0111\u1ec9nh A v\u00e0 \u0111\u1ec9nh B.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 V\u00ec hai \u0111\u01b0\u1eddng th\u1eb3ng a v\u00e0 b song song n\u00ean c\u00e1c g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng nhau v\u00e0 c\u00e1c g\u00f3c so le trong b\u1eb1ng nhau:<br \/>\n&#8211; G\u00f3c \u0111\u1ed3ng v\u1ecb cho tr\u01b0\u1edbc b\u1eb1ng 70\u00b0, suy ra t\u1ea5t c\u1ea3 c\u00e1c g\u00f3c \u0111\u1ed3ng v\u1ecb kh\u00e1c c\u0169ng b\u1eb1ng <code>70\u00b0<\/code>.<br \/>\n\u2022 T\u00ednh c\u00e1c g\u00f3c t\u1ea1i \u0111\u1ec9nh A:<br \/>\n&#8211; G\u00f3c \u0111\u1ed1i \u0111\u1ec9nh v\u1edbi g\u00f3c 70\u00b0 c\u0169ng b\u1eb1ng <code>70\u00b0<\/code>.<\/p>\n<p style=\"margin: 0;\">&#8211; G\u00f3c k\u1ec1 b\u00f9 v\u1edbi g\u00f3c 70\u00b0 b\u1eb1ng <code>180\u00b0 - 70\u00b0 = 110\u00b0<\/code>.<br \/>\n\u2022 T\u00ednh c\u00e1c g\u00f3c t\u1ea1i \u0111\u1ec9nh B:<br \/>\n&#8211; Do t\u00ednh ch\u1ea5t hai \u0111\u01b0\u1eddng th\u1eb3ng song song, c\u00e1c g\u00f3c t\u1ea1i \u0111\u1ec9nh B t\u01b0\u01a1ng \u1ee9ng b\u1eb1ng c\u00e1c g\u00f3c t\u1ea1i \u0111\u1ec9nh A (c\u00e1c g\u00f3c \u0111\u1ed3ng v\u1ecb b\u1eb1ng 70\u00b0 v\u00e0 110\u00b0, c\u00e1c g\u00f3c so le trong c\u0169ng t\u01b0\u01a1ng \u1ee9ng b\u1eb1ng 70\u00b0 v\u00e0 110\u00b0).<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>C\u00e1c g\u00f3c trong h\u00ecnh c\u00f3 s\u1ed1 \u0111o l\u00e0 70\u00b0 v\u00e0 110\u00b0<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 3: \u0110\u1ecaNH L\u00cd V\u00c0 CH\u1ee8NG MINH \u0110\u1ecaNH L\u00cd --><\/p>\n<h2 id=\"muc-13-dinh-li-va-chung-minh-dinh-li\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">\u0110\u1ecbnh l\u00ed v\u00e0 ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">C\u1ea5u tr\u00fac \u0111\u1ecbnh l\u00ed v\u00e0 ph\u01b0\u01a1ng ph\u00e1p ch\u1ee9ng minh h\u00ecnh h\u1ecdc<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>\u0110\u1ecbnh l\u00ed l\u00e0 g\u00ec?<\/strong> L\u00e0 m\u1ed9t kh\u1eb3ng \u0111\u1ecbnh \u0111\u01b0\u1ee3c suy ra l\u00e0 \u0111\u00fang d\u1ef1a tr\u00ean c\u00e1c suy lu\u1eadn logic t\u1eeb nh\u1eefng ki\u1ebfn th\u1ee9c \u0111\u00e3 bi\u1ebft tr\u01b0\u1edbc \u0111\u00f3.<\/li>\n<li><strong>C\u1ea5u tr\u00fac c\u1ee7a m\u1ed9t \u0111\u1ecbnh l\u00ed:<\/strong> G\u1ed3m hai ph\u1ea7n ch\u00ednh:\n<ul>\n<li><strong>Gi\u1ea3 thi\u1ebft (GT):<\/strong> \u0110i\u1ec1u cho tr\u01b0\u1edbc (\u0111i\u1ec1u ki\u1ec7n ban \u0111\u1ea7u).<\/li>\n<li><strong>K\u1ebft lu\u1eadn (KL):<\/strong> \u0110i\u1ec1u c\u1ea7n suy ra (kh\u1eb3ng \u0111\u1ecbnh ph\u1ea3i ch\u1ee9ng minh).<\/li>\n<\/ul>\n<\/li>\n<li><strong>Ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed:<\/strong> L\u00e0 qu\u00e1 tr\u00ecnh d\u00f9ng l\u1eadp lu\u1eadn logic \u0111\u1ec3 suy ra k\u1ebft lu\u1eadn t\u1eeb gi\u1ea3 thi\u1ebft, m\u1ed7i b\u01b0\u1edbc suy lu\u1eadn ph\u1ea3i c\u00f3 c\u0103n c\u1ee9 ch\u00ednh \u0111\u00e1ng (d\u1ef1a v\u00e0o \u0111\u1ecbnh ngh\u0129a, ti\u00ean \u0111\u1ec1 ho\u1eb7c \u0111\u1ecbnh l\u00ed \u0111\u00e3 h\u1ecdc).<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi vi\u1ebft ch\u1ee9ng minh h\u00ecnh h\u1ecdc:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean vi\u1ebft ph\u1ea7n t\u00f3m t\u1eaft gi\u1ea3 thi\u1ebft &#8211; k\u1ebft lu\u1eadn (GT &#8211; KL) ho\u1eb7c trong c\u00e1c b\u01b0\u1edbc l\u1eadp lu\u1eadn kh\u00f4ng ghi r\u00f5 c\u0103n c\u1ee9 \u0111\u1ecbnh l\u00ed\/t\u00ednh ch\u1ea5t \u1edf ngo\u1eb7c \u0111\u01a1n ph\u00eda sau.<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: Ch\u1ee9ng minh hai tia ph\u00e2n gi\u00e1c c\u1ee7a hai g\u00f3c k\u1ec1 b\u00f9 vu\u00f4ng g\u00f3c<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Ch\u1ee9ng minh r\u1eb1ng hai tia ph\u00e2n gi\u00e1c c\u1ee7a hai g\u00f3c k\u1ec1 b\u00f9 th\u00ec vu\u00f4ng g\u00f3c v\u1edbi nhau.<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 B\u01b0\u1edbc 1: Vi\u1ebft gi\u1ea3 thi\u1ebft v\u00e0 k\u1ebft lu\u1eadn (GT &#8211; KL):<br \/>\n&#8211; GT: G\u00f3c xOy v\u00e0 g\u00f3c yOz l\u00e0 hai g\u00f3c k\u1ec1 b\u00f9. Tia Om l\u00e0 ph\u00e2n gi\u00e1c g\u00f3c xOy, tia On l\u00e0 ph\u00e2n gi\u00e1c g\u00f3c yOz.<br \/>\n&#8211; KL: <code>Om vu\u00f4ng g\u00f3c v\u1edbi On<\/code> (t\u1ee9c g\u00f3c mOn = 90\u00b0).<br \/>\n\u2022 B\u01b0\u1edbc 2:<\/p>\n<p style=\"margin: 0;\">Tr\u00ecnh b\u00e0y ch\u1ee9ng minh:<br \/>\n&#8211; V\u00ec g\u00f3c xOy v\u00e0 g\u00f3c yOz l\u00e0 hai g\u00f3c k\u1ec1 b\u00f9 n\u00ean <code>g\u00f3c xOy + g\u00f3c yOz = 180\u00b0<\/code>.<br \/>\n&#8211; V\u00ec Om l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c xOy n\u00ean <code>g\u00f3c mOy = 1\/2 \u00b7 g\u00f3c xOy<\/code>.<br \/>\n&#8211; V\u00ec On l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c yOz n\u00ean <code>g\u00f3c nOy = 1\/2 \u00b7 g\u00f3c yOz<\/code>.<\/p>\n<p style=\"margin: 0;\">&#8211; Do tia Oy n\u1eb1m gi\u1eefa hai tia Om v\u00e0 On, s\u1ed1 \u0111o g\u00f3c mOn l\u00e0:<br \/>\n<code>g\u00f3c mOn = g\u00f3c mOy + g\u00f3c nOy = 1\/2 \u00b7 g\u00f3c xOy + 1\/2 \u00b7 g\u00f3c yOz = 1\/2 \u00b7 (g\u00f3c xOy + g\u00f3c yOz)<\/code>.<br \/>\n&#8211; Thay t\u1ed5ng s\u1ed1 \u0111o b\u1eb1ng 180\u00b0 v\u00e0o bi\u1ec3u th\u1ee9c:<\/p>\n<p style=\"margin: 0;\"><code>g\u00f3c mOn = 1\/2 \u00b7 180\u00b0 = 90\u00b0<\/code>.<br \/>\n&#8211; Do \u0111\u00f3 \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a Om vu\u00f4ng g\u00f3c v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a On (\u0111i\u1ec1u ph\u1ea3i ch\u1ee9ng minh).<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>\u0110\u00e3 ch\u1ee9ng minh g\u00f3c mOn b\u1eb1ng 90\u00b0<\/strong>.<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: PH\u1ea6N II - G\u00d3C V\u00c0 \u0110\u01af\u1edcNG TH\u1eb2NG SONG SONG TO\u00c1N 7 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U: PH\u1ea6N III - H\u00ccNH H\u1eccC TR\u1ef0C QUAN \u2013 H\u00ccNH KH\u1ed0I TO\u00c1N 7 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- BANNER PH\u1ea6N III --><\/p>\n<div style=\"background: linear-gradient(135deg, #0056b3, #0080ff); color: #ffffff; padding: 18px 24px; border-radius: 8px; margin-top: 35px; margin-bottom: 30px;\">\n<h2 id=\"muc-14-phan-iii-hinh-hoc-truc-quan-hinh-khoi\" style=\"color: #ffffff; margin: 0; font-size: 22px; text-transform: uppercase; letter-spacing: 0.5px;\">Ph\u1ea7n III: H\u00ecnh H\u1ecdc Tr\u1ef1c Quan \u2013 H\u00ecnh Kh\u1ed1i<\/h2>\n<\/div>\n<p><!-- B\u1ea2NG T\u00d3M T\u1eaeT C\u00d4NG TH\u1ee8C H\u00ccNH KH\u1ed0I --><\/p>\n<h3 style=\"color: #2b6cb0; font-size: 18px; margin-top: 25px; margin-bottom: 15px;\">B\u1ea3ng t\u00f3m t\u1eaft c\u00f4ng th\u1ee9c di\u1ec7n t\u00edch xung quanh v\u00e0 th\u1ec3 t\u00edch<\/h3>\n<div style=\"overflow-x: auto; margin: 15px 0 25px 0;\">\n<table style=\"table-layout: auto; font-size: 15px; width: 100%; border-collapse: collapse; border: 1px solid #cbd5e0; text-align: left;\">\n<thead style=\"background-color: #edf2f7;\">\n<tr>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; width: 34%;\">H\u00ecnh kh\u1ed1i<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; width: 33%;\">Di\u1ec7n t\u00edch xung quanh (S<sub>xq<\/sub>)<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; color: #0056b3; width: 33%;\">Th\u1ec3 t\u00edch (V)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">H\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt<br \/>\n<span style=\"font-size: 13px; font-weight: normal; color: #4a5568;\">(chi\u1ec1u d\u00e0i a, chi\u1ec1u r\u1ed9ng b, chi\u1ec1u cao c)<\/span><\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0;\">S<sub>xq<\/sub> = 2 \u00b7 (a + b) \u00b7 c<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0;\">V = a \u00b7 b \u00b7 c<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">H\u00ecnh l\u1eadp ph\u01b0\u01a1ng<br \/>\n<span style=\"font-size: 13px; font-weight: normal; color: #4a5568;\">(c\u1ea1nh a)<\/span><\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0;\">S<sub>xq<\/sub> = 4 \u00b7 a<sup>2<\/sup><\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0;\">V = a<sup>3<\/sup><\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0; font-weight: bold;\">L\u0103ng tr\u1ee5 \u0111\u1ee9ng (tam gi\u00e1c \/ t\u1ee9 gi\u00e1c)<br \/>\n<span style=\"font-size: 13px; font-weight: normal; color: #4a5568;\">(chu vi \u0111\u00e1y C<sub>\u0111\u00e1y<\/sub>, di\u1ec7n t\u00edch \u0111\u00e1y S<sub>\u0111\u00e1y<\/sub>, chi\u1ec1u cao h)<\/span><\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0;\">S<sub>xq<\/sub> = C<sub>\u0111\u00e1y<\/sub> \u00b7 h<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 10px 12px; border: 1px solid #cbd5e0;\">V = S<sub>\u0111\u00e1y<\/sub> \u00b7 h<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 1: H\u00ccNH H\u1ed8P CH\u1eee NH\u1eacT, H\u00ccNH L\u1eacP PH\u01af\u01a0NG --><\/p>\n<h2 id=\"muc-15-hinh-hop-chu-nhat-hinh-lap-phuong\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">H\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt, h\u00ecnh l\u1eadp ph\u01b0\u01a1ng<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">C\u1ea5u tr\u00fac, c\u00f4ng th\u1ee9c v\u00e0 b\u00e0i to\u00e1n th\u1ef1c t\u1ebf<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>C\u00e1c y\u1ebfu t\u1ed1 c\u01a1 b\u1ea3n:<\/strong> H\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 8 \u0111\u1ec9nh, 12 c\u1ea1nh, 6 m\u1eb7t l\u00e0 c\u00e1c h\u00ecnh ch\u1eef nh\u1eadt (hai m\u1eb7t \u0111\u00e1y \u0111\u1ed1i di\u1ec7n b\u1eb1ng nhau) v\u00e0 4 \u0111\u01b0\u1eddng ch\u00e9o c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m. H\u00ecnh l\u1eadp ph\u01b0\u01a1ng l\u00e0 h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt \u0111\u1eb7c bi\u1ec7t c\u00f3 6 m\u1eb7t \u0111\u1ec1u l\u00e0 h\u00ecnh vu\u00f4ng b\u1eb1ng nhau.<\/li>\n<li><strong>C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n:<\/strong>\n<ul>\n<li>\u0110\u1ed1i v\u1edbi h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 c\u00e1c k\u00edch th\u01b0\u1edbc d\u00e0i a, r\u1ed9ng b, cao c: Di\u1ec7n t\u00edch xung quanh <code>S<sub>xq<\/sub> = 2 \u00b7 (a + b) \u00b7 c<\/code> ; Th\u1ec3 t\u00edch <code>V = a \u00b7 b \u00b7 c<\/code>.<\/li>\n<li>\u0110\u1ed1i v\u1edbi h\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u1ea1nh a: Di\u1ec7n t\u00edch xung quanh <code>S<sub>xq<\/sub> = 4 \u00b7 a<sup>2<\/sup><\/code> ; Th\u1ec3 t\u00edch <code>V = a<sup>3<\/sup><\/code>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p v\u1ec1 \u0111\u01a1n v\u1ecb \u0111o:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Qu\u00ean \u0111\u1ed5i \u0111\u1ed3ng nh\u1ea5t \u0111\u01a1n v\u1ecb \u0111o c\u1ee7a c\u00e1c k\u00edch th\u01b0\u1edbc tr\u01b0\u1edbc khi t\u00ednh to\u00e1n (v\u00ed d\u1ee5 chi\u1ec1u d\u00e0i \u0111o b\u1eb1ng m\u00e9t nh\u01b0ng chi\u1ec1u cao \u0111o b\u1eb1ng centim\u00e9t), ho\u1eb7c nh\u1ea7m l\u1eabn \u0111\u01a1n v\u1ecb di\u1ec7n t\u00edch (cm<sup>2<\/sup>) v\u1edbi \u0111\u01a1n v\u1ecb th\u1ec3 t\u00edch (cm<sup>3<\/sup>).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: B\u00e0i to\u00e1n th\u1ef1c t\u1ebf t\u00ednh th\u1ec3 t\u00edch b\u1ec3 n\u01b0\u1edbc h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> M\u1ed9t b\u1ec3 n\u01b0\u1edbc h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 c\u00e1c k\u00edch th\u01b0\u1edbc trong l\u00f2ng b\u1ec3 l\u00e0: chi\u1ec1u d\u00e0i 2 m\u00e9t, chi\u1ec1u r\u1ed9ng 1,5 m\u00e9t v\u00e0 chi\u1ec1u cao 1 m\u00e9t. T\u00ednh th\u1ec3 t\u00edch n\u01b0\u1edbc t\u1ed1i \u0111a m\u00e0 b\u1ec3 c\u00f3 th\u1ec3 ch\u1ee9a \u0111\u01b0\u1ee3c (t\u00ednh theo \u0111\u01a1n v\u1ecb m\u00e9t kh\u1ed1i v\u00e0 l\u00edt, bi\u1ebft 1 m\u00e9t kh\u1ed1i b\u1eb1ng 1000 l\u00edt).<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 \u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt:<br \/>\n<code>V = a \u00b7 b \u00b7 c = 2 \u00b7 1,5 \u00b7 1<\/code><br \/>\n<code>V = 3 (m\u00e9t kh\u1ed1i)<\/code>.<br \/>\n\u2022 \u0110\u1ed5i \u0111\u01a1n v\u1ecb sang l\u00edt:<br \/>\n<code>3 m\u00e9t kh\u1ed1i = 3 \u00b7 1000 = 3000 (l\u00edt)<\/code>.<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>Th\u1ec3 t\u00edch b\u1ec3 b\u1eb1ng 3 m\u00e9t kh\u1ed1i (t\u01b0\u01a1ng \u0111\u01b0\u01a1ng 3000 l\u00edt)<\/strong>.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 2: L\u0102NG TR\u1ee4 \u0110\u1ee8NG TAM GI\u00c1C, L\u0102NG TR\u1ee4 \u0110\u1ee8NG T\u1ee8 GI\u00c1C --><\/p>\n<h2 id=\"muc-16-lang-tru-dung-tam-giac-lang-tru-dung-tu-giac\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">L\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c, l\u0103ng tr\u1ee5 \u0111\u1ee9ng t\u1ee9 gi\u00e1c<\/h2>\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 20px;\">\u0110\u1eb7c \u0111i\u1ec3m c\u1ea5u t\u1ea1o v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n<\/h3>\n<ul style=\"padding-left: 20px;\">\n<li><strong>\u0110\u1eb7c \u0111i\u1ec3m c\u1ea5u t\u1ea1o:<\/strong> H\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng c\u00f3 hai m\u1eb7t \u0111\u00e1y l\u00e0 hai \u0111a gi\u00e1c b\u1eb1ng nhau n\u1eb1m \u1edf hai m\u1eb7t ph\u1eb3ng song song, c\u00e1c m\u1eb7t b\u00ean l\u00e0 c\u00e1c h\u00ecnh ch\u1eef nh\u1eadt vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t \u0111\u00e1y. Chi\u1ec1u cao c\u1ee7a l\u0103ng tr\u1ee5 \u0111\u1ee9ng ch\u00ednh l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ee7a c\u1ea1nh b\u00ean.<\/li>\n<li><strong>C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n di\u1ec7n t\u00edch v\u00e0 th\u1ec3 t\u00edch:<\/strong>\n<ul>\n<li>Di\u1ec7n t\u00edch xung quanh b\u1eb1ng chu vi m\u1eb7t \u0111\u00e1y nh\u00e2n v\u1edbi chi\u1ec1u cao: <code>S<sub>xq<\/sub> = C<sub>\u0111\u00e1y<\/sub> \u00b7 h<\/code>.<\/li>\n<li>Th\u1ec3 t\u00edch b\u1eb1ng di\u1ec7n t\u00edch m\u1eb7t \u0111\u00e1y nh\u00e2n v\u1edbi chi\u1ec1u cao: <code>V = S<sub>\u0111\u00e1y<\/sub> \u00b7 h<\/code>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><!-- H\u1ed8P L\u1ed6I SAI TH\u01af\u1edcNG G\u1eb6P --><\/p>\n<div style=\"background-color: #fff5f5; border-left: 4px solid #e53e3e; padding: 14px 18px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"margin: 0 0 6px 0; font-weight: bold; color: #c53030;\">\u26a0\ufe0f L\u1ed7i sai th\u01b0\u1eddng g\u1eb7p khi t\u00ednh di\u1ec7n t\u00edch \u0111\u00e1y l\u0103ng tr\u1ee5:<\/p>\n<ul style=\"margin: 0; padding-left: 20px; font-size: 15px;\">\n<li>Nh\u1ea7m l\u1eabn gi\u1eefa chu vi \u0111\u00e1y (d\u00f9ng \u0111\u1ec3 t\u00ednh di\u1ec7n t\u00edch xung quanh) v\u1edbi di\u1ec7n t\u00edch \u0111\u00e1y (d\u00f9ng \u0111\u1ec3 t\u00ednh th\u1ec3 t\u00edch), ho\u1eb7c d\u00f9ng sai c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c (qu\u00ean h\u1ec7 s\u1ed1 1\/2 khi \u0111\u00e1y l\u00e0 h\u00ecnh tam gi\u00e1c).<\/li>\n<\/ul>\n<\/div>\n<p><!-- V\u00cd D\u1ee4 M\u1eaaU --><\/p>\n<div style=\"background-color: #f7fafc; border-left: 4px solid #0056b3; padding: 16px 20px; border-radius: 4px; margin: 18px 0;\">\n<p style=\"font-weight: bold; color: #0056b3; margin: 0 0 8px 0;\">V\u00ed d\u1ee5 m\u1eabu gi\u1ea3i chi ti\u1ebft: T\u00ednh th\u1ec3 t\u00edch l\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c<\/p>\n<p style=\"margin: 0 0 6px 0;\"><strong>\u0110\u1ec1 b\u00e0i:<\/strong> Cho m\u1ed9t l\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c c\u00f3 chi\u1ec1u cao b\u1eb1ng 7 cm. \u0110\u00e1y l\u00e0 m\u1ed9t tam gi\u00e1c vu\u00f4ng c\u00f3 \u0111\u1ed9 d\u00e0i hai c\u1ea1nh g\u00f3c vu\u00f4ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 3 cm v\u00e0 4 cm. T\u00ednh di\u1ec7n t\u00edch xung quanh v\u00e0 th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u00f3 (bi\u1ebft c\u1ea1nh c\u00f2n l\u1ea1i c\u1ee7a tam gi\u00e1c \u0111\u00e1y b\u1eb1ng 5 cm).<\/p>\n<p style=\"margin: 0;\"><strong>L\u1eddi gi\u1ea3i chi ti\u1ebft:<\/strong><br \/>\n\u2022 T\u00ednh chu vi \u0111\u00e1y \u0111\u1ec3 t\u00ecm di\u1ec7n t\u00edch xung quanh:<br \/>\n&#8211; Chu vi tam gi\u00e1c \u0111\u00e1y: <code>C<sub>\u0111\u00e1y<\/sub> = 3 + 4 + 5 = 12 (cm)<\/code>.<br \/>\n&#8211; Di\u1ec7n t\u00edch xung quanh: <code>S<sub>xq<\/sub> = C<sub>\u0111\u00e1y<\/sub> \u00b7 h = 12 \u00b7 7 = 84 (cm<sup>2<\/sup>)<\/code>.<br \/>\n\u2022 T\u00ednh di\u1ec7n t\u00edch \u0111\u00e1y v\u00e0 th\u1ec3 t\u00edch l\u0103ng tr\u1ee5:<br \/>\n&#8211; Di\u1ec7n t\u00edch tam gi\u00e1c vu\u00f4ng \u0111\u00e1y:<\/p>\n<p style=\"margin: 0;\"><code>S<sub>\u0111\u00e1y<\/sub> = 1\/2 \u00b7 3 \u00b7 4 = 6 (cm<sup>2<\/sup>)<\/code>.<br \/>\n&#8211; Th\u1ec3 t\u00edch h\u00ecnh l\u0103ng tr\u1ee5: <code>V = S<sub>\u0111\u00e1y<\/sub> \u00b7 h = 6 \u00b7 7 = 42 (cm<sup>3<\/sup>)<\/code>.<br \/>\n\u2022 <em>\u0110\u00e1p s\u1ed1:<\/em> <strong>Di\u1ec7n t\u00edch xung quanh b\u1eb1ng 84 cm<sup>2<\/sup> v\u00e0 th\u1ec3 t\u00edch b\u1eb1ng 42 cm<sup>3<\/sup><\/strong>.<\/p>\n<\/div>\n<p><!-- L\u01afU \u00dd \/ INTERNAL LINK BOX --><\/p>\n<div style=\"background-color: #edf2f7; border-left: 4px solid #0056b3; padding: 14px 18px; border-radius: 4px; margin-top: 25px;\">\n<p style=\"margin: 0; font-size: 15px; color: #2d3748;\"><strong>\ud83d\udca1 L\u1eddi khuy\u00ean t\u1eeb chuy\u00ean gia NaviEdu:<\/strong> H\u00ecnh h\u1ecdc tr\u1ef1c quan v\u00e0 c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf v\u1ec1 h\u00ecnh kh\u1ed1i chi\u1ebfm t\u1ec9 tr\u1ecdng \u0111i\u1ec3m s\u1ed1 quan tr\u1ecdng trong b\u00e0i ki\u1ec3m tra gi\u1eefa k\u00ec 1 To\u00e1n 7. N\u1ebfu con \u0111ang g\u1eb7p kh\u00f3 kh\u0103n trong vi\u1ec7c ghi nh\u1edb c\u00f4ng th\u1ee9c ho\u1eb7c \u00e1p d\u1ee5ng v\u00e0o b\u00e0i to\u00e1n th\u1ef1c t\u1ebf, ba m\u1eb9 h\u00e3y tham kh\u1ea3o ngay l\u1ed9 tr\u00ecnh <a style=\"color: #0056b3; font-weight: bold; text-decoration: underline;\" href=\"https:\/\/navi.edu.vn\/mat-goc-toan\/lop-7\">l\u1ea5y l\u1ea1i g\u1ed1c To\u00e1n 7<\/a> t\u1ea1i NaviEdu \u0111\u1ec3 h\u1ed7 tr\u1ee3 con t\u1ef1 tin b\u1ee9t ph\u00e1 \u0111i\u1ec3m s\u1ed1!<\/p>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC: PH\u1ea6N III - H\u00ccNH H\u1eccC TR\u1ef0C QUAN \u2013 H\u00ccNH KH\u1ed0I TO\u00c1N 7 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U PH\u1ea6N IV: L\u1ecaCH \u00d4N T\u1eacP 7 NG\u00c0Y & \u0110\u1ec0 THI M\u1eaaU TO\u00c1N 7 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<p><!-- BANNER PH\u1ea6N IV --><\/p>\n<div style=\"background: linear-gradient(135deg, #0056b3, #0080ff); color: #ffffff; padding: 18px 24px; border-radius: 8px; margin-top: 35px; margin-bottom: 30px;\">\n<h2 id=\"muc-17-phan-iv-lich-on-tap-7-ngay-de-thi-mau\" style=\"color: #ffffff; margin: 0; font-size: 22px; text-transform: uppercase; letter-spacing: 0.5px;\">Ph\u1ea7n IV: L\u1ecbch \u00d4n T\u1eadp 7 Ng\u00e0y &amp; \u0110\u1ec1 Thi M\u1eabu<\/h2>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 1: L\u1ecaCH \u00d4N T\u1eacP 7 NG\u00c0Y --><\/p>\n<p style=\"margin: 0 0 16px 0;\">Khi \u0111\u00e3 \u0111i h\u1ebft c\u00e1c ch\u1ee7 \u0111\u1ec1 trong \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7, ba m\u1eb9 c\u00f3 th\u1ec3 d\u00f9ng l\u1ecbch 7 ng\u00e0y d\u01b0\u1edbi \u0111\u00e2y \u0111\u1ec3 c\u00f9ng con h\u1ec7 th\u1ed1ng l\u1ea1i ki\u1ebfn th\u1ee9c v\u00e0 luy\u1ec7n \u0111\u1ec1 tr\u01b0\u1edbc ng\u00e0y thi.<\/p>\n<h2 id=\"muc-18-lich-on-tap-giua-ki-1-toan-7-trong-7-ngay-giup-con-tu-tin-da\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">L\u1ecbch \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7 trong 7 ng\u00e0y gi\u00fap con t\u1ef1 tin \u0111\u1ea1t \u0111i\u1ec3m cao<\/h2>\n<p>\u0110\u1ec3 gi\u00fap h\u1ecdc sinh THCS \u00f4n luy\u1ec7n hi\u1ec7u qu\u1ea3, n\u1eafm v\u1eefng to\u00e0n b\u1ed9 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m v\u00e0 l\u00e0m quen v\u1edbi \u00e1p l\u1ef1c ph\u00f2ng thi, \u0111\u1ed9i ng\u0169 chuy\u00ean m\u00f4n t\u1ea1i NaviEdu x\u00e2y d\u1ef1ng th\u1eddi gian bi\u1ec3u \u00f4n t\u1eadp n\u01b0\u1edbc r\u00fat trong 7 ng\u00e0y (m\u1ed7i ng\u00e0y t\u1eeb 45 \u2013 60 ph\u00fat):<\/p>\n<div style=\"overflow-x: auto; margin: 20px 0;\">\n<table style=\"min-width: 640px; table-layout: fixed; font-size: 15px; width: 100%; border-collapse: collapse; border: 1px solid #cbd5e0; text-align: left;\">\n<colgroup>\n<col style=\"width: 16%;\" \/>\n<col style=\"width: 48%;\" \/>\n<col style=\"width: 36%;\" \/><\/colgroup>\n<thead style=\"background-color: #edf2f7;\">\n<tr>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; color: #0056b3; width: 18%;\">Th\u1eddi gian<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; color: #0056b3; width: 47%;\">N\u1ed9i dung \u00f4n<\/th>\n<th style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; color: #0056b3; width: 35%;\">M\u1ee5c ti\u00eau (45\u201360 ph\u00fat\/ng\u00e0y)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 1<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">S\u1ed1 h\u1eefu t\u1ec9, c\u1ed9ng tr\u1eeb nh\u00e2n chia.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Th\u00e0nh th\u1ea1o quy t\u1eafc c\u1ed9ng tr\u1eeb ph\u00e2n s\u1ed1, so s\u00e1nh s\u1ed1 h\u1eefu t\u1ec9 v\u00e0 t\u00ednh nhanh h\u1ee3p l\u00ed.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 2<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">L\u0169y th\u1eeba, quy t\u1eafc d\u1ea5u ngo\u1eb7c v\u00e0 chuy\u1ec3n v\u1ebf, t\u00ecm x.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">N\u1eafm ch\u1eafc c\u00f4ng th\u1ee9c l\u0169y th\u1eeba, quy t\u1eafc ph\u00e1 ngo\u1eb7c \u0111\u1ed5i d\u1ea5u v\u00e0 gi\u1ea3i th\u1ea1o b\u00e0i to\u00e1n t\u00ecm x.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 3<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">S\u1ed1 th\u1eadp ph\u00e2n, s\u1ed1 v\u00f4 t\u1ec9, c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc, gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">\u00d4n k\u1ef9 c\u00e1ch l\u00e0m tr\u00f2n s\u1ed1, t\u00ednh c\u0103n b\u1eadc hai s\u1ed1 h\u1ecdc v\u00e0 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 4<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">G\u00f3c k\u1ec1 b\u00f9, \u0111\u1ed1i \u0111\u1ec9nh, tia ph\u00e2n gi\u00e1c; \u0111\u01b0\u1eddng th\u1eb3ng song song.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">V\u1eadn d\u1ee5ng linh ho\u1ea1t t\u00ednh ch\u1ea5t g\u00f3c \u0111\u1eb7c bi\u1ec7t, ti\u00ean \u0111\u1ec1 Euclid v\u00e0 c\u00e1c g\u00f3c t\u1ea1o b\u1edfi \u0111\u01b0\u1eddng th\u1eb3ng song song.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 5<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">\u0110\u1ecbnh l\u00ed v\u00e0 ch\u1ee9ng minh; h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt, l\u1eadp ph\u01b0\u01a1ng, l\u0103ng tr\u1ee5 \u0111\u1ee9ng.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">L\u00e0m quen c\u00e1ch vi\u1ebft gi\u1ea3 thi\u1ebft &#8211; k\u1ebft lu\u1eadn, ch\u1ee9ng minh h\u00ecnh h\u1ecdc v\u00e0 t\u00ednh di\u1ec7n t\u00edch, th\u1ec3 t\u00edch h\u00ecnh kh\u1ed1i.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 6<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">L\u00e0m 2 \u0111\u1ec1 m\u1eabu b\u1ea5m gi\u1edd 90 ph\u00fat.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">T\u1eadp d\u01b0\u1ee3t kh\u00f4ng kh\u00ed ph\u00f2ng thi th\u1eadt, r\u00e8n k\u1ef9 n\u0103ng ph\u00e2n b\u1ed5 th\u1eddi gian h\u1ee3p l\u00fd gi\u1eefa tr\u1eafc nghi\u1ec7m v\u00e0 t\u1ef1 lu\u1eadn.<\/td>\n<\/tr>\n<tr>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0; font-weight: bold;\">Ng\u00e0y 7<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Xem l\u1ea1i l\u1ed7i sai, ngh\u1ec9 ng\u01a1i.<\/td>\n<td style=\"word-break: normal; overflow-wrap: normal; hyphens: none; padding: 12px 14px; border: 1px solid #cbd5e0;\">Kh\u1eafc ph\u1ee5c tri\u1ec7t \u0111\u1ec3 c\u00e1c l\u1ed7i t\u00ednh to\u00e1n s\u01a1 \u0111\u1eb3ng, \u00f4n l\u1ea1i c\u00f4ng th\u1ee9c c\u1ed1t l\u00f5i v\u00e0 gi\u1eef t\u00e2m l\u00fd tho\u1ea3i m\u00e1i.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><!-- H\u1ed8P G\u1ee2I \u00dd \/ BLOG LINK --><\/p>\n<div style=\"background-color: #edf2f7; border-left: 4px solid #0056b3; padding: 14px 18px; border-radius: 4px; margin: 20px 0;\">\n<p style=\"margin: 0; font-size: 15px; color: #2d3748;\"><strong>\ud83d\udca1 L\u1eddi khuy\u00ean cho h\u1ecdc sinh THCS:<\/strong> Giai \u0111o\u1ea1n chuy\u1ec3n ti\u1ebfp l\u00ean l\u1edbp 7 \u0111\u00f2i h\u1ecfi t\u01b0 duy logic ch\u1eb7t ch\u1ebd h\u01a1n r\u1ea5t nhi\u1ec1u. Ba m\u1eb9 v\u00e0 h\u1ecdc sinh c\u00f3 th\u1ec3 tham kh\u1ea3o th\u00eam c\u00e1c ph\u01b0\u01a1ng ph\u00e1p <a style=\"color: #0056b3; font-weight: bold; text-decoration: underline;\" href=\"https:\/\/navi.edu.vn\/blog\/cach-hoc-toan-hieu-qua-thu-tu-hoc-chuan\/\">c\u00e1ch h\u1ecdc To\u00e1n hi\u1ec7u qu\u1ea3<\/a> \u0111\u1ec3 t\u1ed1i \u01b0u h\u00f3a n\u0103ng l\u1ef1c ti\u1ebfp thu m\u1ed7i ng\u00e0y.<\/p>\n<\/div>\n<p><!-- CH\u1ee6 \u0110\u1ec0 2: T\u1ea2I \u0110\u1ec0 C\u01af\u01a0NG V\u00c0 \u0110\u1ec0 THI M\u1eaaU --><\/p>\n<h2 id=\"muc-19-tai-de-cuong-on-tap-giua-ki-1-toan-7-va-de-thi-mau-pdf-co-da\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">T\u1ea3i \u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7 v\u00e0 \u0111\u1ec1 thi m\u1eabu (PDF c\u00f3 \u0111\u00e1p \u00e1n)<\/h2>\n<p>Nh\u1eb1m gi\u00fap h\u1ecdc sinh l\u1edbp 7 c\u1ecd x\u00e1t v\u1edbi c\u1ea5u tr\u00fac \u0111\u1ec1 ki\u1ec3m tra \u0111\u1ecbnh k\u00ec chu\u1ea9n m\u1ef1c, \u0111\u1ed9i ng\u0169 gi\u00e1o vi\u00ean chuy\u00ean m\u00f4n t\u1ea1i NaviEdu \u0111\u00e3 bi\u00ean so\u1ea1n tr\u1ecdn b\u1ed9 t\u00e0i li\u1ec7u \u0111\u1ed9c quy\u1ec1n b\u00e1m s\u00e1t Th\u00f4ng t\u01b0 22:<\/p>\n<div style=\"background-color: #f7fafc; border: 1px solid #e2e8f0; border-radius: 8px; padding: 22px; margin: 20px 0;\">\n<h3 style=\"color: #2b6cb0; font-size: 17px; margin-top: 0; margin-bottom: 12px;\">T\u00f3m t\u1eaft c\u1ea5u tr\u00fac b\u1ed9 \u0111\u1ec1 m\u1eabu NaviEdu:<\/h3>\n<ul style=\"padding-left: 20px; margin-bottom: 15px;\">\n<li><strong>Ph\u1ea7n Tr\u1eafc nghi\u1ec7m (3.0 \u0111i\u1ec3m):<\/strong> G\u1ed3m 12 c\u00e2u h\u1ecfi kh\u00e1ch quan (nhi\u1ec1u l\u1ef1a ch\u1ecdn), ki\u1ec3m tra nhanh nh\u1eadn bi\u1ebft v\u00e0 th\u00f4ng hi\u1ec3u to\u00e0n b\u1ed9 ki\u1ebfn th\u1ee9c s\u1ed1 h\u1eefu t\u1ec9, s\u1ed1 th\u1ef1c, g\u00f3c v\u00e0 h\u00ecnh kh\u1ed1i.<\/li>\n<li><strong>Ph\u1ea7n T\u1ef1 lu\u1eadn (7.0 \u0111i\u1ec3m):<\/strong> \u0110\u01b0\u1ee3c chia th\u00e0nh c\u00e1c b\u00e0i c\u1ee5 th\u1ec3:\n<ul>\n<li><em>B\u00e0i 1 (1.5 \u0111i\u1ec3m):<\/em> Th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh s\u1ed1 h\u1eefu t\u1ec9, t\u00ednh h\u1ee3p l\u00ed (\u00e1p d\u1ee5ng t\u00ednh ch\u1ea5t ph\u00e2n ph\u1ed1i).<\/li>\n<li><em>B\u00e0i 2 (1.5 \u0111i\u1ec3m):<\/em> T\u00ecm x (\u00e1p d\u1ee5ng quy t\u1eafc chuy\u1ec3n v\u1ebf, l\u0169y th\u1eeba ho\u1eb7c gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i).<\/li>\n<li><em>B\u00e0i 3 (1.0 \u0111i\u1ec3m):<\/em> T\u00ednh s\u1ed1 \u0111o g\u00f3c d\u1ef1a v\u00e0o t\u00ednh ch\u1ea5t g\u00f3c k\u1ec1 b\u00f9, \u0111\u1ed1i \u0111\u1ec9nh ho\u1eb7c \u0111\u01b0\u1eddng th\u1eb3ng song song.<\/li>\n<li><em>B\u00e0i 4 (1.5 \u0111i\u1ec3m):<\/em> B\u00e0i to\u00e1n h\u00ecnh h\u1ecdc c\u00f3 l\u1eadp lu\u1eadn ch\u1ee9ng minh (ch\u1ee9ng minh song song ho\u1eb7c t\u00ednh ch\u1ea5t tia ph\u00e2n gi\u00e1c, GT-KL).<\/li>\n<li><em>B\u00e0i 5 (1.0 \u0111i\u1ec3m):<\/em> B\u00e0i to\u00e1n th\u1ef1c t\u1ebf v\u1ec1 h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt, h\u00ecnh l\u1eadp ph\u01b0\u01a1ng ho\u1eb7c l\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c (t\u00ednh di\u1ec7n t\u00edch xung quanh, th\u1ec3 t\u00edch).<\/li>\n<li><em>B\u00e0i 6 (0.5 \u0111i\u1ec3m &#8211; V\u1eadn d\u1ee5ng cao):<\/em> B\u00e0i to\u00e1n n\u00e2ng cao, ch\u1ee9ng minh \u0111\u1eb3ng th\u1ee9c ph\u00e2n s\u1ed1 ho\u1eb7c t\u00ecm gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t, nh\u1ecf nh\u1ea5t.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p style=\"margin-top: 15px; margin-bottom: 20px; color: #4a5568;\">To\u00e0n b\u1ed9 t\u00e0i li\u1ec7u bao g\u1ed3m t\u00f3m t\u1eaft l\u00fd thuy\u1ebft tr\u1ecdng t\u00e2m, h\u1ec7 th\u1ed1ng b\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n theo t\u1eebng chuy\u00ean \u0111\u1ec1 v\u00e0 03 \u0111\u1ec1 thi th\u1eed chu\u1ea9n format 90 ph\u00fat c\u00f3 k\u00e8m b\u1ea3ng \u0111\u00e1p \u00e1n, h\u01b0\u1edbng d\u1eabn gi\u1ea3i chi ti\u1ebft t\u1eebng b\u01b0\u1edbc gi\u00fap con t\u1ef1 h\u1ecdc hi\u1ec7u qu\u1ea3 t\u1ea1i nh\u00e0:<\/p>\n<div style=\"text-align: center; margin-top: 25px; padding-top: 18px; border-top: 1px dashed #cbd5e0;\"><a style=\"background-color: #d9534f; color: #ffffff; padding: 13px 30px; text-decoration: none; border-radius: 6px; font-weight: bold; font-size: 16px; display: inline-block; box-shadow: 0 2px 5px rgba(217,83,79,0.3);\" href=\"https:\/\/navi.edu.vn\/thu-vien\/danh-muc-tai-lieu\/lop-7\/\">\ud83d\udce5 T\u1ea2I TR\u1eccN B\u1ed8 \u0110\u1ec0 C\u01af\u01a0NG &amp; \u0110\u1ec0 M\u1eaaU TO\u00c1N 7 (PDF)<br \/>\n<\/a><\/p>\n<p style=\"margin-top: 12px; font-size: 14px; color: #4a5568;\">(T\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c c\u1eadp nh\u1eadt mi\u1ec5n ph\u00ed t\u1ea1i kho <a style=\"color: #0056b3; font-weight: bold; text-decoration: underline;\" href=\"https:\/\/navi.edu.vn\/thu-vien\/danh-muc-tai-lieu\/lop-7\/\">th\u01b0 vi\u1ec7n h\u1ecdc li\u1ec7u NaviEdu<\/a>)<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC PH\u1ea6N IV: L\u1ecaCH \u00d4N T\u1eacP 7 NG\u00c0Y & \u0110\u1ec0 THI M\u1eaaU TO\u00c1N 7 --><\/p>\n<p><!-- B\u1eaeT \u0110\u1ea6U K\u1ebeT B\u00c0I V\u00c0 KH\u1ed0I CTA WORDPRESS TO\u00c1N 7 --><\/p>\n<div class=\"naviedu-content-section\" style=\"font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif; line-height: 1.8; color: #2d3748; font-size: 16px;\">\n<h2 id=\"muc-20-loi-ket\" style=\"color: #0056b3; border-bottom: 2px solid #e2e8f0; padding-bottom: 8px; margin-top: 35px; font-size: 20px;\">L\u1eddi k\u1ebft<\/h2>\n<p>B\u01b0\u1edbc v\u00e0o ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n 7 v\u1edbi nh\u1eefng b\u01b0\u1edbc chuy\u1ec3n bi\u1ebfn quan tr\u1ecdng t\u1eeb t\u00ednh to\u00e1n \u0111\u1ea1i s\u1ed1 sang t\u01b0 duy l\u1eadp lu\u1eadn h\u00ecnh h\u1ecdc s\u1eafc b\u00e9n \u0111\u00f2i h\u1ecfi c\u00e1c em h\u1ecdc sinh s\u1ef1 t\u1eadp trung v\u00e0 ph\u01b0\u01a1ng ph\u00e1p h\u1ecdc t\u1eadp khoa h\u1ecdc. Vi\u1ec7c ch\u1ee7 \u0111\u1ed9ng r\u00e8n luy\u1ec7n qua h\u1ec7 th\u1ed1ng b\u00e0i t\u1eadp \u0111a d\u1ea1ng s\u1ebd l\u00e0 n\u1ec1n t\u1ea3ng v\u1eefng ch\u1eafc gi\u00fap c\u00e1c em v\u01b0\u1ee3t qua m\u1ecdi th\u1eed th\u00e1ch tr\u00ean gh\u1ebf nh\u00e0 tr\u01b0\u1eddng.<\/p>\n<p>Hy v\u1ecdng r\u1eb1ng b\u1ed9 <strong>\u0111\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7<\/strong> do \u0111\u1ed9i ng\u0169 chuy\u00ean m\u00f4n NaviEdu bi\u00ean so\u1ea1n s\u1ebd l\u00e0 ng\u01b0\u1eddi b\u1ea1n \u0111\u1ed3ng h\u00e0nh tin c\u1eady, gi\u00fap ba m\u1eb9 v\u00e0 c\u00e1c con g\u1ee1 r\u1ed1i m\u1ecdi kh\u00f3 kh\u0103n. Ch\u00fac c\u00e1c em gi\u1eef v\u1eefng tinh th\u1ea7n t\u1ef1 tin, \u00f4n luy\u1ec7n th\u00f4ng minh v\u00e0 \u0111\u1ea1t \u0111i\u1ec3m s\u1ed1 th\u1eadt cao trong k\u00ec thi s\u1eafp t\u1edbi!<\/p>\n<p><!-- KH\u1ed0I CTA WORDPRESS CHU\u1ea8N CHUY\u1ec2N \u0110\u1ed4I --><\/p>\n<div style=\"border: 2px dashed #0056b3; background-color: #f4f8ff; border-radius: 10px; padding: 25px; text-align: center; margin: 35px 0;\">\n<h3 style=\"color: #0056b3; margin-top: 0; font-size: 20px; font-weight: bold;\">B\u1ee9t Ph\u00e1 \u0110i\u1ec3m S\u1ed1 Gi\u1eefa K\u00ec 1 To\u00e1n 7 C\u00f9ng L\u1ed9 Tr\u00ecnh C\u00e1 Nh\u00e2n H\u00f3a T\u1ea1i NaviEdu!<\/h3>\n<p style=\"font-size: 16px; line-height: 1.6; color: #333333; margin-bottom: 20px; max-width: 750px; margin-left: auto; margin-right: auto;\">Ba m\u1eb9 h\u00e3y \u0111\u01b0a con \u0111\u1ebfn c\u01a1 s\u1edf <strong>NaviEdu (33 LK6B M\u1ed7 Lao, L\u00e0ng Vi\u1ec7t Ki\u1ec1u Ch\u00e2u \u00c2u, H\u00e0 \u0110\u00f4ng)<\/strong> \u0111\u1ec3 tham gia l\u00e0m b\u00e0i \u0111\u00e1nh gi\u00e1 n\u0103ng l\u1ef1c mi\u1ec5n ph\u00ed b\u1eb1ng Math AI v\u00e0 nh\u1eadn l\u1ed9 tr\u00ecnh h\u1ecdc &#8220;may \u0111o&#8221; ri\u00eang bi\u1ec7t cho ch\u00ednh con ngay h\u00f4m nay!<\/p>\n<div><a style=\"background-color: #0056b3; color: #ffffff; padding: 13px 30px; text-decoration: none; border-radius: 6px; font-weight: bold; font-size: 16px; display: inline-block; box-shadow: 0 2px 4px rgba(0,86,179,0.2);\" href=\"https:\/\/navi.edu.vn\/giai-phap\/dang-ky-tu-van?utm_campaign=All.Blog._Organic.Dieuttm_Testtoan7.cta.2610_._.&amp;utm_medium=Dieuttm\" target=\"_blank\" rel=\"noopener\">L\u00c0M B\u00c0I \u0110\u00c1NH GI\u00c1 N\u0102NG L\u1ef0C MI\u1ec4N PH\u00cd<\/a><\/div>\n<\/div>\n<\/div>\n<p><!-- K\u1ebeT TH\u00daC K\u1ebeT B\u00c0I V\u00c0 KH\u1ed0I CTA WORDPRESS TO\u00c1N 7 --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ec1 c\u01b0\u01a1ng \u00f4n t\u1eadp gi\u1eefa k\u00ec 1 To\u00e1n 7 (2026\u20132027): ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m, d\u1ea1ng b\u00e0i hay g\u1eb7p, \u0111\u1ec1 m\u1eabu c\u00f3 \u0111\u00e1p \u00e1n, l\u1ecbch \u00f4n 7 ng\u00e0y v\u00e0 file PDF t\u1ea3i mi\u1ec5n ph\u00ed.<\/p>\n","protected":false},"author":2,"featured_media":2896,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[6],"tags":[],"_links":{"self":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts\/2874"}],"collection":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/comments?post=2874"}],"version-history":[{"count":5,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts\/2874\/revisions"}],"predecessor-version":[{"id":2899,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/posts\/2874\/revisions\/2899"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/media\/2896"}],"wp:attachment":[{"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/media?parent=2874"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/categories?post=2874"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/navi.edu.vn\/blog\/wp-json\/wp\/v2\/tags?post=2874"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}