{"id":567214,"date":"2026-07-22T15:19:13","date_gmt":"2026-07-22T08:19:13","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=567214"},"modified":"2026-07-22T16:28:02","modified_gmt":"2026-07-22T09:28:02","slug":"duong-trung-binh","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/duong-trung-binh\/","title":{"rendered":"\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c v\u00e0 h\u00ecnh thang: l\u00fd thuy\u1ebft v\u00e0 v\u00ed d\u1ee5"},"content":{"rendered":"<p>\u0110\u01b0\u1eddng trung b\u00ecnh l\u00e0 m\u1ed9t trong nh\u1eefng kh\u00e1i ni\u1ec7m n\u1ec1n t\u1ea3ng c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh H\u00ecnh h\u1ecdc l\u1edbp 8, xu\u1ea5t hi\u1ec7n trong c\u1ea3 tam gi\u00e1c l\u1eabn h\u00ecnh thang. Hi\u1ec3u \u0111\u00fang \u0111\u1ecbnh ngh\u0129a v\u00e0 hai c\u00f4ng th\u1ee9c li\u00ean quan gi\u00fap b\u1ea1n gi\u1ea3i nhanh nhi\u1ec1u d\u1ea1ng b\u00e0i ch\u1ee9ng minh song song, t\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng m\u00e0 kh\u00f4ng c\u1ea7n \u0111o tr\u1ef1c ti\u1ebfp. N\u1ed9i dung sau t\u1ed5ng h\u1ee3p \u0111\u1ecbnh ngh\u0129a, \u0111\u1ecbnh l\u00fd, d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft, v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i t\u1eebng b\u01b0\u1edbc v\u00e0 b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng \u0111\u1ec3 b\u1ea1n \u00f4n t\u1eadp hi\u1ec7u qu\u1ea3 h\u01a1n.<\/p>\n<h2>\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c l\u00e0 g\u00ec?<\/h2>\n<p>\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c l\u00e0 \u0111o\u1ea1n th\u1eb3ng n\u1ed1i trung \u0111i\u1ec3m hai c\u1ea1nh c\u1ee7a tam gi\u00e1c \u0111\u00f3.<\/p>\n<p>Trong m\u1ed9t tam gi\u00e1c b\u1ea5t k\u1ef3, m\u1ed7i c\u1eb7p c\u1ea1nh \u0111\u1ec1u c\u00f3 m\u1ed9t trung \u0111i\u1ec3m, v\u00e0 \u0111o\u1ea1n th\u1eb3ng n\u1ed1i hai trung \u0111i\u1ec3m n\u00e0y \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh \u1ee9ng v\u1edbi c\u1ea1nh c\u00f2n l\u1ea1i. V\u00ec tam gi\u00e1c c\u00f3 ba c\u1ea1nh n\u00ean s\u1ebd c\u00f3 ba \u0111\u01b0\u1eddng trung b\u00ecnh, m\u1ed7i \u0111\u01b0\u1eddng song song v\u00e0 b\u1eb1ng n\u1eeda c\u1ea1nh \u0111\u1ed1i di\u1ec7n v\u1edbi n\u00f3. \u0110\u00e2y l\u00e0 c\u00f4ng c\u1ee5 quen thu\u1ed9c \u0111\u1ec3 ch\u1ee9ng minh hai \u0111o\u1ea1n th\u1eb3ng song song ho\u1eb7c t\u00ednh \u0111\u1ed9 d\u00e0i m\u1ed9t c\u1ea1nh khi kh\u00f4ng th\u1ec3 \u0111o tr\u1ef1c ti\u1ebfp.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-569055 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-1.jpg\" alt=\"duong-trung-binh-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>\u0110\u1ecbnh l\u00fd v\u00e0 d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c<\/h2>\n<p>\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c song song v\u1edbi c\u1ea1nh th\u1ee9 ba v\u00e0 c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng m\u1ed9t n\u1eeda c\u1ea1nh \u0111\u00f3.<\/p>\n<p><strong>\u0110\u1ecbnh l\u00fd 1 (t\u00ednh ch\u1ea5t):<\/strong> N\u1ebfu D v\u00e0 E l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB v\u00e0 AC trong tam gi\u00e1c ABC th\u00ec DE l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh \u1ee9ng v\u1edbi c\u1ea1nh BC. Khi \u0111\u00f3 DE song song v\u1edbi BC v\u00e0 DE = BC\/2.<\/p>\n<p><strong>\u0110\u1ecbnh l\u00fd 2 (d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft):<\/strong> \u0110\u01b0\u1eddng th\u1eb3ng \u0111i qua trung \u0111i\u1ec3m m\u1ed9t c\u1ea1nh c\u1ee7a tam gi\u00e1c v\u00e0 song song v\u1edbi c\u1ea1nh th\u1ee9 hai th\u00ec \u0111i qua trung \u0111i\u1ec3m c\u1ea1nh th\u1ee9 ba. T\u00ednh ch\u1ea5t n\u00e0y th\u01b0\u1eddng \u0111\u01b0\u1ee3c d\u00f9ng \u0111\u1ec3 ch\u1ee9ng minh m\u1ed9t \u0111i\u1ec3m l\u00e0 trung \u0111i\u1ec3m m\u00e0 kh\u00f4ng c\u1ea7n \u0111o \u0111\u1ea1c.<\/p>\n<ul>\n<li>Mu\u1ed1n x\u00e1c \u0111\u1ecbnh m\u1ed9t \u0111o\u1ea1n th\u1eb3ng c\u00f3 ph\u1ea3i \u0111\u01b0\u1eddng trung b\u00ecnh hay kh\u00f4ng, ch\u1ec9 c\u1ea7n ki\u1ec3m tra hai \u0111\u1ea7u \u0111o\u1ea1n th\u1eb3ng c\u00f3 ph\u1ea3i trung \u0111i\u1ec3m c\u1ee7a hai c\u1ea1nh trong c\u00f9ng m\u1ed9t tam gi\u00e1c hay kh\u00f4ng.<\/li>\n<li>N\u1ebfu \u0111\u1ec1 b\u00e0i cho m\u1ed9t \u0111o\u1ea1n th\u1eb3ng \u0111i qua trung \u0111i\u1ec3m m\u1ed9t c\u1ea1nh v\u00e0 song song v\u1edbi c\u1ea1nh kh\u00e1c, \u0111\u00f3 c\u0169ng l\u00e0 d\u1ea5u hi\u1ec7u \u0111\u1ec3 suy ra \u0111\u01b0\u1eddng trung b\u00ecnh.<\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"size-full wp-image-569056 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-2.jpg\" alt=\"duong-trung-binh-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang l\u00e0 g\u00ec?<\/h2>\n<p>\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang l\u00e0 \u0111o\u1ea1n th\u1eb3ng n\u1ed1i trung \u0111i\u1ec3m hai c\u1ea1nh b\u00ean, song song v\u1edbi hai \u0111\u00e1y v\u00e0 b\u1eb1ng n\u1eeda t\u1ed5ng hai \u0111\u00e1y.<\/p>\n<p>X\u00e9t h\u00ecnh thang ABCD c\u00f3 AB song song CD, trong \u0111\u00f3 AB l\u00e0 \u0111\u00e1y nh\u1ecf v\u00e0 CD l\u00e0 \u0111\u00e1y l\u1edbn. G\u1ecdi M v\u00e0 N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a hai c\u1ea1nh b\u00ean AD v\u00e0 BC. \u0110o\u1ea1n th\u1eb3ng MN ch\u00ednh l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang. \u0110\u1ecbnh l\u00fd cho bi\u1ebft MN song song v\u1edbi c\u1ea3 AB v\u00e0 CD, \u0111\u1ed3ng th\u1eddi \u0111\u1ed9 d\u00e0i MN b\u1eb1ng n\u1eeda t\u1ed5ng hai \u0111\u00e1y.<\/p>\n<p>C\u00f4ng th\u1ee9c: MN = (AB + CD) \/ 2.<\/p>\n<p><strong>D\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft:<\/strong> n\u1ebfu m\u1ed9t \u0111o\u1ea1n th\u1eb3ng \u0111i qua trung \u0111i\u1ec3m m\u1ed9t c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh thang v\u00e0 song song v\u1edbi hai \u0111\u00e1y th\u00ec n\u00f3 c\u0169ng \u0111i qua trung \u0111i\u1ec3m c\u1ea1nh b\u00ean c\u00f2n l\u1ea1i \u2014 \u0111\u00f3 ch\u00ednh l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh.<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-569057 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-3.jpg\" alt=\"duong-trung-binh-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>B\u1ea3ng so s\u00e1nh \u0111\u01b0\u1eddng trung b\u00ecnh tam gi\u00e1c v\u00e0 h\u00ecnh thang<\/h2>\n<p>Hai kh\u00e1i ni\u1ec7m d\u00f9ng chung t\u00ean g\u1ecdi nh\u01b0ng c\u00e1ch x\u00e1c \u0111\u1ecbnh v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh kh\u00e1c nhau, b\u1ea3ng d\u01b0\u1edbi \u0111\u00e2y t\u00f3m t\u1eaft \u0111i\u1ec3m kh\u00e1c bi\u1ec7t ch\u00ednh.<\/p>\n<table>\n<thead>\n<tr>\n<th>Ti\u00eau ch\u00ed<\/th>\n<th>\u0110\u01b0\u1eddng trung b\u00ecnh tam gi\u00e1c<\/th>\n<th>\u0110\u01b0\u1eddng trung b\u00ecnh h\u00ecnh thang<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>N\u1ed1i trung \u0111i\u1ec3m c\u1ee7a<\/td>\n<td>Hai c\u1ea1nh b\u1ea5t k\u1ef3 c\u1ee7a tam gi\u00e1c<\/td>\n<td>Hai c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh thang<\/td>\n<\/tr>\n<tr>\n<td>S\u1ed1 l\u01b0\u1ee3ng trong m\u1ed9t h\u00ecnh<\/td>\n<td>Ba \u0111\u01b0\u1eddng trung b\u00ecnh<\/td>\n<td>M\u1ed9t \u0111\u01b0\u1eddng trung b\u00ecnh<\/td>\n<\/tr>\n<tr>\n<td>Quan h\u1ec7 song song<\/td>\n<td>Song song v\u1edbi c\u1ea1nh th\u1ee9 ba<\/td>\n<td>Song song v\u1edbi c\u1ea3 hai \u0111\u00e1y<\/td>\n<\/tr>\n<tr>\n<td>C\u00f4ng th\u1ee9c \u0111\u1ed9 d\u00e0i<\/td>\n<td>B\u1eb1ng n\u1eeda c\u1ea1nh th\u1ee9 ba<\/td>\n<td>B\u1eb1ng n\u1eeda t\u1ed5ng hai \u0111\u00e1y<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>V\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft<\/h2>\n<p>Ba v\u00ed d\u1ee5 d\u01b0\u1edbi \u0111\u00e2y minh h\u1ecda c\u00e1ch \u00e1p d\u1ee5ng t\u1eebng c\u00f4ng th\u1ee9c theo t\u1eebng b\u01b0\u1edbc c\u1ee5 th\u1ec3.<\/p>\n<p><strong>V\u00ed d\u1ee5 1:<\/strong> Tam gi\u00e1c ABC c\u00f3 c\u1ea1nh BC = 10cm. G\u1ecdi D, E l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB v\u00e0 AC. T\u00ednh \u0111\u1ed9 d\u00e0i DE.<\/p>\n<p><em>L\u1eddi gi\u1ea3i:<\/em> V\u00ec D, E l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m AB, AC n\u00ean DE l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c ABC \u1ee9ng v\u1edbi c\u1ea1nh BC. Suy ra DE = BC\/2 = 10\/2 = 5cm.<\/p>\n<p><strong>V\u00ed d\u1ee5 2:<\/strong> H\u00ecnh thang ABCD c\u00f3 AB song song CD, \u0111\u00e1y nh\u1ecf AB = 6cm, \u0111\u00e1y l\u1edbn CD = 10cm. G\u1ecdi M, N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m hai c\u1ea1nh b\u00ean AD, BC. T\u00ednh \u0111\u1ed9 d\u00e0i MN.<\/p>\n<p><em>L\u1eddi gi\u1ea3i:<\/em> M, N l\u00e0 trung \u0111i\u1ec3m hai c\u1ea1nh b\u00ean n\u00ean MN l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang. Suy ra MN = (AB + CD)\/2 = (6 + 10)\/2 = 8cm.<\/p>\n<p><strong>V\u00ed d\u1ee5 3:<\/strong> M\u1ed9t tam gi\u00e1c c\u00f3 \u0111\u01b0\u1eddng trung b\u00ecnh d\u00e0i 7cm. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh song song v\u1edbi \u0111\u01b0\u1eddng trung b\u00ecnh \u0111\u00f3.<\/p>\n<p><em>L\u1eddi gi\u1ea3i:<\/em> Theo t\u00ednh ch\u1ea5t, \u0111\u01b0\u1eddng trung b\u00ecnh b\u1eb1ng n\u1eeda c\u1ea1nh th\u1ee9 ba n\u00ean c\u1ea1nh th\u1ee9 ba = 2 \u00d7 7 = 14cm.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/he-thuc-luong-trong-tam-giac\/\">Xem th\u00eam: H\u1ec7 th\u1ee9c l\u01b0\u1ee3ng trong tam gi\u00e1c: \u0111\u1ecbnh l\u00fd cosin, sin, di\u1ec7n t\u00edch<\/a><\/p>\n<h2>B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i<\/h2>\n<p>B\u1ea1n c\u00f3 th\u1ec3 t\u1ef1 luy\u1ec7n th\u00eam v\u1edbi c\u00e1c b\u00e0i t\u1eadp sau, m\u1ed7i b\u00e0i k\u00e8m l\u1eddi gi\u1ea3i \u0111\u1ec3 \u0111\u1ed1i chi\u1ebfu k\u1ebft qu\u1ea3.<\/p>\n<ul>\n<li><strong>B\u00e0i 1:<\/strong> Tam gi\u00e1c c\u00f3 c\u1ea1nh \u0111\u00e1y 14cm. T\u00ednh \u0111\u01b0\u1eddng trung b\u00ecnh \u1ee9ng v\u1edbi c\u1ea1nh \u0111\u00f3. <em>L\u1eddi gi\u1ea3i:<\/em> \u0111\u01b0\u1eddng trung b\u00ecnh = 14\/2 = 7cm.<\/li>\n<li><strong>B\u00e0i 2:<\/strong> \u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c d\u00e0i 6cm. T\u00ednh c\u1ea1nh song song v\u1edbi n\u00f3. <em>L\u1eddi gi\u1ea3i:<\/em> c\u1ea1nh \u0111\u00f3 = 2 \u00d7 6 = 12cm.<\/li>\n<li><strong>B\u00e0i 3:<\/strong> H\u00ecnh thang c\u00f3 \u0111\u00e1y l\u1edbn 12cm, \u0111\u00e1y nh\u1ecf 8cm. T\u00ednh \u0111\u01b0\u1eddng trung b\u00ecnh. <em>L\u1eddi gi\u1ea3i:<\/em> m = (12 + 8)\/2 = 10cm.<\/li>\n<li><strong>B\u00e0i 4:<\/strong> \u0110\u01b0\u1eddng trung b\u00ecnh h\u00ecnh thang b\u1eb1ng 9cm, \u0111\u00e1y nh\u1ecf 6cm. T\u00ednh \u0111\u00e1y l\u1edbn. <em>L\u1eddi gi\u1ea3i:<\/em> t\u1eeb m = (a + b)\/2 suy ra a + b = 18, \u0111\u00e1y l\u1edbn = 18 \u2212 6 = 12cm.<\/li>\n<li><strong>B\u00e0i 5:<\/strong> Tam gi\u00e1c \u0111\u1ec1u c\u00f3 c\u1ea1nh 16cm. T\u00ednh \u0111\u1ed9 d\u00e0i m\u1ed7i \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c. <em>L\u1eddi gi\u1ea3i:<\/em> ba c\u1ea1nh b\u1eb1ng nhau n\u00ean c\u1ea3 ba \u0111\u01b0\u1eddng trung b\u00ecnh \u0111\u1ec1u b\u1eb1ng 16\/2 = 8cm.<\/li>\n<li><strong>B\u00e0i 6 (tr\u1eafc nghi\u1ec7m):<\/strong> \u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c c\u00f3 c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng d\u00e0i 20cm l\u00e0 bao nhi\u00eau? A. 20cm B. 40cm C. 10cm D. 5cm. <em>\u0110\u00e1p \u00e1n:<\/em> C, v\u00ec \u0111\u01b0\u1eddng trung b\u00ecnh = 20\/2 = 10cm.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-569060 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-5.jpg\" alt=\"duong-trung-binh-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>\u1ee8ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a \u0111\u01b0\u1eddng trung b\u00ecnh<\/h2>\n<p>\u0110\u01b0\u1eddng trung b\u00ecnh kh\u00f4ng ch\u1ec9 l\u00e0 l\u00fd thuy\u1ebft m\u00e0 c\u00f2n l\u00e0 c\u00f4ng c\u1ee5 gi\u1ea3i to\u00e1n quen thu\u1ed9c trong nhi\u1ec1u d\u1ea1ng b\u00e0i h\u00ecnh h\u1ecdc.<\/p>\n<p>B\u1ea1n c\u00f3 th\u1ec3 d\u00f9ng \u0111\u01b0\u1eddng trung b\u00ecnh \u0111\u1ec3 ch\u1ee9ng minh hai \u0111o\u1ea1n th\u1eb3ng song song m\u00e0 kh\u00f4ng c\u1ea7n \u0111o \u0111\u1ea1c, t\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng trong c\u00e1c b\u00e0i to\u00e1n kh\u00f3 ti\u1ebfp c\u1eadn tr\u1ef1c ti\u1ebfp, ho\u1eb7c l\u00e0m b\u01b0\u1edbc trung gian trong c\u00e1c b\u00e0i to\u00e1n v\u1ec1 t\u1ec9 l\u1ec7 v\u00e0 di\u1ec7n t\u00edch. \u1ede c\u00e1c ch\u01b0\u01a1ng sau, kh\u00e1i ni\u1ec7m n\u00e0y c\u00f2n xu\u1ea5t hi\u1ec7n khi h\u1ecdc v\u1ec1 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang c\u00e2n hay khi ch\u1ee9ng minh c\u00e1c \u0111\u1ecbnh l\u00fd li\u00ean quan \u0111\u1ebfn tr\u1ecdng t\u00e2m v\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c.<\/p>\n<h2>Ph\u00e2n bi\u1ec7t \u0111\u01b0\u1eddng trung b\u00ecnh v\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn<\/h2>\n<p>Hai kh\u00e1i ni\u1ec7m n\u00e0y d\u1ec5 g\u00e2y nh\u1ea7m l\u1eabn v\u00ec \u0111\u1ec1u g\u1eafn v\u1edbi trung \u0111i\u1ec3m nh\u01b0ng b\u1ea3n ch\u1ea5t kh\u00e1c nhau.<\/p>\n<p>\u0110\u01b0\u1eddng trung b\u00ecnh n\u1ed1i trung \u0111i\u1ec3m c\u1ee7a hai c\u1ea1nh trong tam gi\u00e1c v\u00e0 song song v\u1edbi c\u1ea1nh c\u00f2n l\u1ea1i. Trong khi \u0111\u00f3, \u0111\u01b0\u1eddng trung tuy\u1ebfn n\u1ed1i m\u1ed9t \u0111\u1ec9nh v\u1edbi trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh \u0111\u1ed1i di\u1ec7n. M\u1ed9t tam gi\u00e1c c\u00f3 ba \u0111\u01b0\u1eddng trung tuy\u1ebfn, ch\u00fang lu\u00f4n c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m g\u1ecdi l\u00e0 tr\u1ecdng t\u00e2m \u2014 \u0111i\u1ec3m chia m\u1ed7i \u0111\u01b0\u1eddng trung tuy\u1ebfn theo t\u1ec9 l\u1ec7 2:1 t\u00ednh t\u1eeb \u0111\u1ec9nh. V\u00ec v\u1eady khi l\u00e0m b\u00e0i, b\u1ea1n c\u1ea7n \u0111\u1ecdc k\u1ef9 \u0111\u1ec1 \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111o\u1ea1n th\u1eb3ng c\u1ea7n t\u00ecm l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh hay \u0111\u01b0\u1eddng trung tuy\u1ebfn tr\u01b0\u1edbc khi \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tam-giac-dong-dang-la-gi\/\">Xem th\u00eam: Tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng l\u00e0 g\u00ec? C\u00e1c tr\u01b0\u1eddng h\u1ee3p v\u00e0 t\u00ednh ch\u1ea5t<\/a><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-569058 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-4.jpg\" alt=\"duong-trung-binh-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/duong-trung-binh-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 \u0111\u01b0\u1eddng trung b\u00ecnh<\/h2>\n<h3>\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c l\u00e0 g\u00ec?<\/h3>\n<p>L\u00e0 \u0111o\u1ea1n th\u1eb3ng n\u1ed1i trung \u0111i\u1ec3m hai c\u1ea1nh c\u1ee7a tam gi\u00e1c, song song v\u00e0 b\u1eb1ng n\u1eeda c\u1ea1nh th\u1ee9 ba.<\/p>\n<h3>T\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c l\u00e0 g\u00ec?<\/h3>\n<p>Song song v\u1edbi c\u1ea1nh th\u1ee9 ba v\u00e0 c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng n\u1eeda c\u1ea1nh \u0111\u00f3.<\/p>\n<h3>\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang t\u00ednh th\u1ebf n\u00e0o?<\/h3>\n<p>B\u1eb1ng n\u1eeda t\u1ed5ng hai \u0111\u00e1y, theo c\u00f4ng th\u1ee9c MN = (AB + CD)\/2.<\/p>\n<h3>M\u1ed9t tam gi\u00e1c c\u00f3 m\u1ea5y \u0111\u01b0\u1eddng trung b\u00ecnh?<\/h3>\n<p>C\u00f3 ba \u0111\u01b0\u1eddng trung b\u00ecnh, m\u1ed7i \u0111\u01b0\u1eddng n\u1ed1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed9t c\u1eb7p c\u1ea1nh.<\/p>\n<h3>\u0110\u01b0\u1eddng trung b\u00ecnh d\u00f9ng \u0111\u1ec3 l\u00e0m g\u00ec?<\/h3>\n<p>D\u00f9ng \u0111\u1ec3 ch\u1ee9ng minh hai \u0111o\u1ea1n th\u1eb3ng song song, t\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng v\u00e0 gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc li\u00ean quan \u0111\u1ebfn t\u1ec9 l\u1ec7.<\/p>\n<h3>\u0110\u01b0\u1eddng trung b\u00ecnh kh\u00e1c \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1edf \u0111i\u1ec3m n\u00e0o?<\/h3>\n<p>\u0110\u01b0\u1eddng trung b\u00ecnh n\u1ed1i trung \u0111i\u1ec3m hai c\u1ea1nh, c\u00f2n \u0111\u01b0\u1eddng trung tuy\u1ebfn n\u1ed1i m\u1ed9t \u0111\u1ec9nh v\u1edbi trung \u0111i\u1ec3m c\u1ea1nh \u0111\u1ed1i di\u1ec7n v\u00e0 \u0111i qua tr\u1ecdng t\u00e2m tam gi\u00e1c.<\/p>\n<h3>L\u00e0m sao nh\u1eadn bi\u1ebft m\u1ed9t \u0111o\u1ea1n th\u1eb3ng l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang?<\/h3>\n<p>N\u1ebfu \u0111o\u1ea1n th\u1eb3ng \u0111i qua trung \u0111i\u1ec3m m\u1ed9t c\u1ea1nh b\u00ean v\u00e0 song song v\u1edbi hai \u0111\u00e1y th\u00ec n\u00f3 c\u0169ng \u0111i qua trung \u0111i\u1ec3m c\u1ea1nh b\u00ean c\u00f2n l\u1ea1i \u2014 \u0111\u00f3 ch\u00ednh l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c song song v\u00e0 b\u1eb1ng n\u1eeda c\u1ea1nh th\u1ee9 ba, c\u00f2n \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang song song v\u00e0 b\u1eb1ng n\u1eeda t\u1ed5ng hai \u0111\u00e1y. Ghi nh\u1edb hai \u0111\u1ecbnh l\u00fd n\u00e0y c\u00f9ng d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft s\u1ebd gi\u00fap b\u1ea1n gi\u1ea3i nhanh c\u00e1c b\u00e0i ch\u1ee9ng minh song song v\u00e0 t\u00ednh \u0111\u1ed9 d\u00e0i trong ch\u01b0\u01a1ng tr\u00ecnh H\u00ecnh h\u1ecdc l\u1edbp 8. B\u1ea1n c\u00f3 th\u1ec3 \u00f4n th\u00eam qua c\u00e1c b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cach-tinh-dien-tich-tam-giac-vuong\/\">c\u00e1ch t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c vu\u00f4ng<\/a>, <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-tam-giac\/\">c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c<\/a>, <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cach-tinh-dien-tich-tam-giac-deu\/\">c\u00e1ch t\u00ednh di\u1ec7n t\u00edch tam gi\u00e1c \u0111\u1ec1u<\/a> v\u00e0 <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dinh-ly-talet\/\">\u0111\u1ecbnh l\u00fd Talet<\/a> \u0111\u1ec3 c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c h\u00ecnh h\u1ecdc.<\/p>\n<p><script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"L\u00e0 \u0111o\u1ea1n th\u1eb3ng n\u1ed1i trung \u0111i\u1ec3m hai c\u1ea1nh c\u1ee7a tam gi\u00e1c, song song v\u00e0 b\u1eb1ng n\u1eeda c\u1ea1nh th\u1ee9 ba.\"}},{\"@type\":\"Question\",\"name\":\"T\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Song song v\u1edbi c\u1ea1nh th\u1ee9 ba v\u00e0 c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng n\u1eeda c\u1ea1nh \u0111\u00f3.\"}},{\"@type\":\"Question\",\"name\":\"\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang t\u00ednh th\u1ebf n\u00e0o?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"B\u1eb1ng n\u1eeda t\u1ed5ng hai \u0111\u00e1y, theo c\u00f4ng th\u1ee9c MN = (AB + CD)\/2.\"}},{\"@type\":\"Question\",\"name\":\"M\u1ed9t tam gi\u00e1c c\u00f3 m\u1ea5y \u0111\u01b0\u1eddng trung b\u00ecnh?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"C\u00f3 ba \u0111\u01b0\u1eddng trung b\u00ecnh, m\u1ed7i \u0111\u01b0\u1eddng n\u1ed1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed9t c\u1eb7p c\u1ea1nh.\"}},{\"@type\":\"Question\",\"name\":\"\u0110\u01b0\u1eddng trung b\u00ecnh d\u00f9ng \u0111\u1ec3 l\u00e0m g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"D\u00f9ng \u0111\u1ec3 ch\u1ee9ng minh hai \u0111o\u1ea1n th\u1eb3ng song song, t\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng v\u00e0 gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc li\u00ean quan \u0111\u1ebfn t\u1ec9 l\u1ec7.\"}},{\"@type\":\"Question\",\"name\":\"\u0110\u01b0\u1eddng trung b\u00ecnh kh\u00e1c \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1edf \u0111i\u1ec3m n\u00e0o?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"\u0110\u01b0\u1eddng trung b\u00ecnh n\u1ed1i trung \u0111i\u1ec3m hai c\u1ea1nh, c\u00f2n \u0111\u01b0\u1eddng trung tuy\u1ebfn n\u1ed1i m\u1ed9t \u0111\u1ec9nh v\u1edbi trung \u0111i\u1ec3m c\u1ea1nh \u0111\u1ed1i di\u1ec7n v\u00e0 \u0111i qua tr\u1ecdng t\u00e2m tam gi\u00e1c.\"}},{\"@type\":\"Question\",\"name\":\"L\u00e0m sao nh\u1eadn bi\u1ebft m\u1ed9t \u0111o\u1ea1n th\u1eb3ng l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"N\u1ebfu \u0111o\u1ea1n th\u1eb3ng \u0111i qua trung \u0111i\u1ec3m m\u1ed9t c\u1ea1nh b\u00ean v\u00e0 song song v\u1edbi hai \u0111\u00e1y th\u00ec n\u00f3 c\u0169ng \u0111i qua trung \u0111i\u1ec3m c\u1ea1nh b\u00ean c\u00f2n l\u1ea1i \u2014 \u0111\u00f3 ch\u00ednh l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh.\"}}]}\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u01b0\u1eddng trung b\u00ecnh l\u00e0 m\u1ed9t trong nh\u1eefng kh\u00e1i ni\u1ec7m n\u1ec1n t\u1ea3ng c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh H\u00ecnh h\u1ecdc l\u1edbp 8, xu\u1ea5t hi\u1ec7n trong c\u1ea3 tam gi\u00e1c l\u1eabn h\u00ecnh thang. Hi\u1ec3u \u0111\u00fang \u0111\u1ecbnh ngh\u0129a v\u00e0 hai c\u00f4ng th\u1ee9c li\u00ean quan gi\u00fap b\u1ea1n gi\u1ea3i nhanh nhi\u1ec1u d\u1ea1ng b\u00e0i ch\u1ee9ng minh song song, t\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n th\u1eb3ng m\u00e0 kh\u00f4ng [&hellip;]<\/p>\n","protected":false},"author":65,"featured_media":569054,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"\u0111\u01b0\u1eddng trung b\u00ecnh","_yoast_wpseo_title":"\u0110\u01b0\u1eddng trung b\u00ecnh tam gi\u00e1c v\u00e0 h\u00ecnh thang","_yoast_wpseo_metadesc":"\u0110\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c v\u00e0 h\u00ecnh thang l\u00e0 g\u00ec, c\u00f4ng th\u1ee9c t\u00ednh, v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft v\u00e0 b\u00e0i t\u1eadp v\u1eadn d\u1ee5ng. 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