{"id":298566,"date":"2023-12-21T21:43:15","date_gmt":"2023-12-21T14:43:15","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=298566"},"modified":"2023-12-21T21:43:17","modified_gmt":"2023-12-21T14:43:17","slug":"duong-trung-tuyen-la-gi","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/duong-trung-tuyen-la-gi\/","title":{"rendered":"\u0110\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec? T\u00ednh ch\u1ea5t, c\u00f4ng th\u1ee9c v\u00e0 b\u00e0i t\u1eadp t\u00ednh \u0111\u01b0\u1eddng trung tuy\u1ebfn"},"content":{"rendered":"<p>\u0110\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m ph\u1ed5 bi\u1ebfn trong h\u00ecnh h\u1ecdc kh\u00f4ng gian v\u00e0 ch\u1ee7 y\u1ebfu \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng trong tam gi\u00e1c. V\u1edbi nh\u1eefng ki\u1ebfn th\u1ee9c v\u1ec1 kh\u00e1i ni\u1ec7m v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n, ch\u00fang ta c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng ch\u00fang \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc li\u00ean quan \u0111\u1ebfn tam gi\u00e1c m\u1ed9t c\u00e1ch d\u1ec5 d\u00e0ng. Trong b\u00e0i vi\u1ebft n\u00e0y, h\u00e3y c\u00f9ng ch\u00fang t\u00f4i kh\u00e1m ph\u00e1 v\u1ec1 <strong>\u0111\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec<\/strong> v\u00e0 c\u00f9ng v\u1edbi m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp \u0111\u1ec3 l\u00e0m quen v\u1edbi ch\u1ee7 \u0111\u1ec1 n\u00e0y.<\/p>\n<h2>\u0110\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec?<\/h2>\n<p>\u0110\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng b\u1ea5t k\u1ef3 \u0111i \u0111i qua trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n th\u1eb3ng \u0111\u00f3. Trong m\u1ed9t tam gi\u00e1c, \u0111\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 m\u1ed9t \u0111o\u1ea1n th\u1eb3ng n\u1ed1i t\u1eeb \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c \u0111\u00f3 \u0111\u1ebfn trung \u0111i\u1ec3m thu\u1ed9c c\u1ea1nh \u0111\u1ed1i di\u1ec7n c\u1ee7a tam gi\u00e1c \u0111\u00f3. M\u1ed7i tam gi\u00e1c c\u00f3 ba \u0111\u01b0\u1eddng trung tuy\u1ebfn v\u00e0 ba \u0111\u01b0\u1eddng trung tuy\u1ebfn n\u00e0y c\u00f9ng c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m g\u1ecdi l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c. Tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c c\u00f3 m\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t \u0111\u1eb7c bi\u1ec7t, ch\u1eb3ng h\u1ea1n nh\u01b0 n\u00f3 c\u00e1ch m\u1ed7i \u0111\u1ec9nh m\u1ed9t kho\u1ea3ng b\u1eb1ng hai ph\u1ea7n ba \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi \u0111\u1ec9nh \u0111\u00f3.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-trung-tuyen-la-gi\/duong-trung-tuyen-la-gi-2\/\" rel=\"attachment wp-att-298687\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-2-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-2-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-298687 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-2.jpg\" alt=\"duong-trung-tuyen-la-gi-2\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-2-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-2-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>\u0110\u01b0\u1eddng trung tuy\u1ebfn c\u00f2n c\u00f3 m\u1ed9t \u0111\u1eb7c \u0111i\u1ec3m quan tr\u1ecdng kh\u00e1c l\u00e0 n\u00f3 chia di\u1ec7n t\u00edch c\u1ee7a tam gi\u00e1c th\u00e0nh hai ph\u1ea7n b\u1eb1ng nhau. Ngo\u00e0i ra, ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u00f2n chia tam gi\u00e1c th\u00e0nh s\u00e1u tam gi\u00e1c nh\u1ecf c\u00f3 di\u1ec7n t\u00edch b\u1eb1ng nhau. \u0110i\u1ec1u n\u00e0y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ch\u1ee9ng minh b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00fd Apollonius ho\u1eb7c b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c v\u1ec1 di\u1ec7n t\u00edch tam gi\u00e1c.<\/p>\n<p>\u0110\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec c\u00f2n c\u00f3 m\u1ed9t s\u1ed1 \u0111\u1eb7c tr\u01b0ng ri\u00eang trong c\u00e1c tam gi\u00e1c \u0111\u1eb7c bi\u1ec7t nh\u01b0 tam gi\u00e1c vu\u00f4ng, tam gi\u00e1c c\u00e2n hay tam gi\u00e1c \u0111\u1ec1u. V\u00ed d\u1ee5, trong tam gi\u00e1c vu\u00f4ng, \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n b\u1eb1ng m\u1ed9t n\u1eeda c\u1ea1nh huy\u1ec1n. Trong tam gi\u00e1c c\u00e2n, \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh \u0111\u00e1y vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh \u0111\u00e1y v\u00e0 chia tam gi\u00e1c th\u00e0nh hai tam gi\u00e1c b\u1eb1ng nhau. Trong tam gi\u00e1c \u0111\u1ec1u, m\u1ed7i \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u0169ng l\u00e0 \u0111\u01b0\u1eddng cao, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c, v\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c.<\/p>\n<h2>T\u00ednh ch\u1ea5t c\u1ee7a \u0111\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec?<\/h2>\n<p>T\u00ednh ch\u1ea5t c\u1ee7a \u0111\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 m\u1ed9t trong nh\u1eefng kh\u00eda c\u1ea1nh quan tr\u1ecdng trong h\u00ecnh h\u1ecdc tam gi\u00e1c. B\u1eb1ng c\u00e1ch kh\u00e1m ph\u00e1 c\u00e1c t\u00ednh ch\u1ea5t c\u1ee7a \u0111\u01b0\u1eddng trung tuy\u1ebfn, ch\u00fang ta c\u00f3 th\u1ec3 hi\u1ec3u s\u00e2u h\u01a1n v\u1ec1 c\u1ea5u tr\u00fac v\u00e0 m\u1ed1i quan h\u1ec7 trong tam gi\u00e1c. \u0110\u01b0\u1eddng trung tuy\u1ebfn c\u00f3 m\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t \u0111\u1eb7c bi\u1ec7t trong c\u00e1c lo\u1ea1i tam gi\u00e1c kh\u00e1c nhau. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 th\u00f4ng tin c\u1ee5 th\u1ec3 t\u00ednh ch\u1ea5t c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0y:<\/p>\n<p>Trong tam gi\u00e1c c\u00e2n, \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh \u0111\u00e1y s\u1ebd vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh \u0111\u00e1y v\u00e0 chia tam gi\u00e1c \u0111\u00f3 th\u00e0nh hai tam gi\u00e1c b\u1eb1ng nhau. Trong tam gi\u00e1c \u0111\u1ec1u, ba \u0111\u01b0\u1eddng trung tuy\u1ebfn \u0111\u1ec1u vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh \u0111\u1ed1i di\u1ec7n v\u00e0 chia tam gi\u00e1c \u0111\u00f3 th\u00e0nh s\u00e1u tam gi\u00e1c \u0111\u1ec1u nh\u1ecf.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-trung-tuyen-la-gi\/duong-trung-tuyen-la-gi-3\/\" rel=\"attachment wp-att-298688\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-3-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-3-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-298688 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-3.jpg\" alt=\"duong-trung-tuyen-la-gi-3\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-3-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-3-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>Trong tam gi\u00e1c vu\u00f4ng, \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n s\u1ebd b\u1eb1ng m\u1ed9t n\u1eeda \u0111\u1ed9 d\u00e0i c\u1ea1nh huy\u1ec1n v\u00e0 chia tam gi\u00e1c vu\u00f4ng th\u00e0nh hai tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng v\u1edbi tam gi\u00e1c ban \u0111\u1ea7u. \u0110\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi m\u1ed9t c\u1ea1nh g\u00f3c vu\u00f4ng s\u1ebd b\u1eb1ng trung b\u00ecnh c\u1ed9ng c\u1ee7a \u0111\u1ed9 d\u00e0i c\u1ea1nh huy\u1ec1n v\u00e0 c\u1ea1nh g\u00f3c vu\u00f4ng \u0111\u1ed1i di\u1ec7n.<\/p>\n<p>\u0110\u1ed1i v\u1edbi tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng th\u00ec t\u1ec9 s\u1ed1 \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh \u0111\u1ed1i di\u1ec7n s\u1ebd b\u1eb1ng t\u1ec9 s\u1ed1 \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng c\u1ee7a hai tam gi\u00e1c. Ngh\u0129a l\u00e0, n\u1ebfu tam gi\u00e1c ABC \u0111\u1ed3ng d\u1ea1ng v\u1edbi tam gi\u00e1c A\u2019B\u2019C\u2019 th\u00ec AD\/BC = A\u2019D\u2019\/B\u2019C\u2019.<\/p>\n<h2>Nh\u1eefng \u0111\u1ecbnh l\u00ed c\u1ee7a \u0111\u01b0\u1eddng trung tuy\u1ebfn trong h\u00ecnh h\u1ecdc<\/h2>\n<p>Sau khi t\u00ecm hi\u1ec3u k\u1ef9 v\u1ec1 \u0111\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec, ta c\u00f3 th\u1ec3 th\u1ea5y \u0111\u01b0\u1ee3c \u0111o\u1ea1n th\u1eb3ng n\u00e0y c\u00f3 vai tr\u00f2 quan tr\u1ecdng trong nghi\u00ean c\u1ee9u tam gi\u00e1c v\u00e0 c\u00f3 m\u1ed9t s\u1ed1 \u0111\u1ecbnh l\u00ed li\u00ean quan \u0111\u1ebfn n\u00f3. M\u1ed7i \u0111\u1ecbnh l\u00fd \u0111\u1ec1u c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng trong nhi\u1ec1u tr\u01b0\u1eddng h\u1ee3p kh\u00e1c nhau. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 ba \u0111\u1ecbnh l\u00ed c\u01a1 b\u1ea3n v\u1ec1 \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c.<\/p>\n<h3>Hai \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c th\u00ec chia nhau m\u1ed9t n\u1eeda v\u1ec1 \u0111\u1ed9 d\u00e0i<\/h3>\n<p>\u0110\u1ecbnh l\u00ed n\u00e0y kh\u1eb3ng \u0111\u1ecbnh r\u1eb1ng hai \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c chia nhau th\u00e0nh hai ph\u1ea7n b\u1eb1ng nhau v\u1ec1 \u0111\u1ed9 d\u00e0i. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn t\u1eeb m\u1ed9t \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c \u0111\u1ebfn trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh \u0111\u1ed1i di\u1ec7n c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng m\u1ed9t n\u1eeda \u0111\u01b0\u1eddng trung tuy\u1ebfn t\u1eeb \u0111\u1ec9nh c\u00f2n l\u1ea1i \u0111\u1ebfn trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh \u0111\u1ed1i di\u1ec7n. \u0110\u1ecbnh l\u00ed tr\u00ean cung c\u1ea5p m\u1ed9t v\u1ea5n \u0111\u1ec1 \u0111\u00e1ng ch\u00fa \u00fd v\u1ec1 m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c \u0111\u01b0\u1eddng trung tuy\u1ebfn v\u00e0 c\u00e1c c\u1ea1nh c\u1ee7a tam gi\u00e1c.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-trung-tuyen-la-gi\/duong-trung-tuyen-la-gi-4\/\" rel=\"attachment wp-att-298689\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-4-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-4-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-298689 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-4.jpg\" alt=\"duong-trung-tuyen-la-gi-4\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-4-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-4-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>\u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 \u0111\u1ecbnh l\u00ed n\u00e0y, h\u00e3y xem x\u00e9t m\u1ed9t tam gi\u00e1c b\u1ea5t k\u1ef3. Gi\u1ea3 s\u1eed ta c\u00f3 m\u1ed9t tam gi\u00e1c ABC b\u1ea5t k\u1ef3 n\u00e0o \u0111\u00f3. \u0110\u01b0\u1eddng trung tuy\u1ebfn t\u1eeb \u0111\u1ec9nh A \u0111\u1ebfn trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh BC s\u1ebd c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng m\u1ed9t n\u1eeda \u0111\u01b0\u1eddng trung tuy\u1ebfn t\u1eeb \u0111\u1ec9nh B \u0111\u1ebfn trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh AC. T\u01b0\u01a1ng t\u1ef1, \u0111\u01b0\u1eddng trung tuy\u1ebfn t\u1eeb \u0111\u1ec9nh A \u0111\u1ebfn trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh AC s\u1ebd c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng m\u1ed9t n\u1eeda \u0111\u01b0\u1eddng trung tuy\u1ebfn t\u1eeb \u0111\u1ec9nh C \u0111\u1ebfn trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh AB. \u0110i\u1ec1u n\u00e0y \u00e1m ch\u1ec9 r\u1eb1ng hai \u0111\u01b0\u1eddng trung tuy\u1ebfn n\u00e0y s\u1ebd chia nhau m\u1ed9t n\u1eeda v\u1ec1 \u0111\u1ed9 d\u00e0i.<\/p>\n<h3>\u0110\u01b0\u1eddng trung tuy\u1ebfn v\u00e0 c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng c\u1ee7a tam gi\u00e1c t\u1ea1o th\u00e0nh m\u1ed9t \u0111o\u1ea1n th\u1eb3ng song song<\/h3>\n<p>\u0110\u1ecbnh l\u00ed n\u00e0y \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1eb1ng \u0111\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a n\u00f3 trong tam gi\u00e1c. T\u1eeb \u0111\u00f3 ta bi\u1ebft \u0111\u01b0\u1ee3c \u0111o\u1ea1n th\u1eb3ng n\u00e0y v\u00e0 c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng c\u1ee7a tam gi\u00e1c l\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng song song. V\u00ec v\u1eady, \u0111\u01b0\u1eddng trung tuy\u1ebfn t\u1eeb m\u1ed9t \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c \u0111\u1ebfn trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh \u0111\u1ed1i di\u1ec7n song song v\u1edbi c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng. \u0110\u1ecbnh l\u00ed n\u00e0y cho th\u1ea5y m\u1ed9t t\u00ednh ch\u1ea5t quan tr\u1ecdng c\u1ee7a \u0111\u01b0\u1eddng trung tuy\u1ebfn v\u00e0 m\u1ed1i quan h\u1ec7 c\u1ee7a n\u00f3 v\u1edbi c\u00e1c c\u1ea1nh c\u1ee7a tam gi\u00e1c.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-trung-tuyen-la-gi\/duong-trung-tuyen-la-gi-5\/\" rel=\"attachment wp-att-298690\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-5.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-5-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-5-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298690 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-5.jpg\" alt=\"duong-trung-tuyen-la-gi-5\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-5-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-5-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>\u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n, x\u00e9t m\u1ed9t tam gi\u00e1c ABC v\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn AH t\u1eeb \u0111\u1ec9nh A \u0111\u1ebfn trung \u0111i\u1ec3m M c\u1ee7a c\u1ea1nh BC. \u0110\u01b0\u1eddng trung tuy\u1ebfn AH v\u00e0 c\u1ea1nh t\u01b0\u01a1ng \u1ee9ng BC t\u1ea1o th\u00e0nh m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng duy nh\u1ea5t v\u00e0 \u0111\u1ecbnh l\u00ed 2 kh\u1eb3ng \u0111\u1ecbnh r\u1eb1ng \u0111\u01b0\u1eddng n\u00e0y l\u00e0 m\u1ed9t \u0111o\u1ea1n th\u1eb3ng song song.<\/p>\n<h3>Ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c giao nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t<\/h3>\n<p>Ba \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c giao nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t, m\u00e0 n\u00f3 ch\u00ednh l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c. Tr\u1ecdng t\u00e2m \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c \u0111o\u1ea1n th\u1eb3ng n\u1ed1i c\u00e1c \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c v\u1edbi trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh \u0111\u1ed1i di\u1ec7n. N\u00f3 l\u00e0 m\u1ed9t \u0111i\u1ec3m \u0111\u1eb7c bi\u1ec7t trong tam gi\u00e1c v\u00ec mang trong m\u00ecnh m\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t \u0111\u00e1ng ch\u00fa \u00fd.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-trung-tuyen-la-gi\/duong-trung-tuyen-la-gi-6\/\" rel=\"attachment wp-att-298691\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-6.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-6-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-6-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298691 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-6.jpg\" alt=\"duong-trung-tuyen-la-gi-6\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-6-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-6-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>Tr\u1ecdng t\u00e2m c\u00f3 m\u1ed9t t\u00ednh ch\u1ea5t \u0111\u1ed9c \u0111\u00e1o l\u00e0 t\u1ed5ng c\u00e1c vect\u01a1 t\u1eeb tr\u1ecdng t\u00e2m \u0111\u1ebfn c\u00e1c \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c b\u1eb1ng vect\u01a1 kh\u00f4ng. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 n\u1ebfu ch\u00fang ta v\u1ebd c\u00e1c vect\u01a1 t\u1eeb tr\u1ecdng t\u00e2m \u0111\u1ebfn c\u00e1c \u0111\u1ec9nh v\u00e0 c\u1ed9ng ch\u00fang l\u1ea1i, t\u1ed5ng k\u1ebft qu\u1ea3 s\u1ebd l\u00e0 vect\u01a1 kh\u00f4ng. \u0110i\u1ec1u n\u00e0y th\u1ec3 hi\u1ec7n s\u1ef1 c\u00e2n b\u1eb1ng c\u1ee7a tam gi\u00e1c v\u00e0 cho th\u1ea5y r\u1eb1ng tr\u1ecdng t\u00e2m n\u1eb1m \u1edf trung t\u00e2m h\u00ecnh h\u1ecdc c\u1ee7a tam gi\u00e1c.<\/p>\n<p>Ngo\u00e0i ra, tr\u1ecdng t\u00e2m c\u0169ng \u0111\u1eb7c bi\u1ec7t v\u00ec n\u00f3 chia ba \u0111\u01b0\u1eddng trung tuy\u1ebfn th\u00e0nh t\u1ef7 l\u1ec7 1:2. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn t\u1eeb tr\u1ecdng t\u00e2m \u0111\u1ebfn m\u1ed9t \u0111\u1ec9nh b\u1ea5t k\u1ef3 s\u1ebd c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng hai l\u1ea7n \u0111\u01b0\u1eddng trung tuy\u1ebfn t\u1eeb tr\u1ecdng t\u00e2m \u0111\u1ebfn trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh \u0111\u1ed1i di\u1ec7n. T\u1ef7 l\u1ec7 n\u00e0y th\u1ec3 hi\u1ec7n m\u1ed9t m\u1ed1i quan h\u1ec7 \u0111\u1eb7c bi\u1ec7t gi\u1eefa tr\u1ecdng t\u00e2m v\u00e0 c\u00e1c \u0111\u01b0\u1eddng trung tuy\u1ebfn, t\u1ea1o ra m\u1ed9t s\u1ef1 ph\u00e2n b\u1ed5 \u0111\u1ec1u v\u00e0 c\u00e2n b\u1eb1ng trong tam gi\u00e1c.<\/p>\n<h2>C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n \u0111\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec?<\/h2>\n<p>\u0110\u1ec3 t\u00ednh to\u00e1n \u0111\u01b0\u1eddng trung tuy\u1ebfn trong tam gi\u00e1c, ch\u00fang ta c\u1ea7n bi\u1ebft c\u00e1c th\u00f4ng tin c\u01a1 b\u1ea3n v\u1ec1 tam gi\u00e1c \u0111\u00f3, bao g\u1ed3m \u0111\u1ed9 d\u00e0i c\u00e1c c\u1ea1nh v\u00e0 t\u1ecda \u0111\u1ed9 c\u00e1c \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c. C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n \u0111\u01b0\u1eddng trung tuy\u1ebfn ph\u1ee5 thu\u1ed9c v\u00e0o c\u00e1c th\u00f4ng tin n\u00e0y v\u00e0 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng d\u1ec5 d\u00e0ng.<\/p>\n<h3>C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u1ea1nh BC<\/h3>\n<p>Gi\u1ea3 s\u1eed ta c\u00f3 tam gi\u00e1c ABC v\u1edbi t\u1ecda \u0111\u1ed9 c\u1ee7a c\u00e1c \u0111\u1ec9nh l\u00e0 A(x1, y1), B(x2, y2), C(x3, y3). \u0110\u1ec3 t\u00ednh to\u00e1n t\u1ecda \u0111\u1ed9 c\u1ee7a \u0111i\u1ec3m D l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh BC, ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c d\u01b0\u1edbi \u0111\u00e2y:<\/p>\n<p>T\u1ecda \u0111\u1ed9 x c\u1ee7a D b\u1eb1ng trung b\u00ecnh c\u1ed9ng c\u1ee7a t\u1ecda \u0111\u1ed9 x c\u1ee7a B v\u00e0 C, t\u1ee9c l\u00e0: xD = (x2 + x3) \/ 2.<\/p>\n<p>T\u1ecda \u0111\u1ed9 y c\u1ee7a D b\u1eb1ng trung b\u00ecnh c\u1ed9ng c\u1ee7a t\u1ecda \u0111\u1ed9 y c\u1ee7a B v\u00e0 C, t\u1ee9c l\u00e0: yD = (y2 + y3) \/ 2.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-trung-tuyen-la-gi\/duong-trung-tuyen-la-gi-7\/\" rel=\"attachment wp-att-298692\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-7.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-7-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-7-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298692 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-7.jpg\" alt=\"duong-trung-tuyen-la-gi-7\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-7-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-7-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>V\u1edbi x l\u00e0 ho\u00e0nh \u0111\u1ed9 c\u1ee7a \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u1ea1nh BC v\u00e0 y l\u00e0 tung \u0111\u1ed9 c\u1ee7a \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u1ea1nh BC. V\u1eady l\u00fac n\u00e0y t\u1ecda \u0111\u1ed9 c\u1ee7a D s\u1ebd \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 D((x2 + x3) \/ 2, (y2 + y3) \/ 2).<\/p>\n<h3>C\u00f4ng th\u1ee9c t\u00ednh to\u00e1n t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u00e1c c\u1ea1nh c\u00f2n l\u1ea1i<\/h3>\n<p>T\u01b0\u01a1ng t\u1ef1 nh\u01b0 tr\u00ean, d\u1ef1a v\u00e0o \u0111\u1ecbnh ngh\u0129a \u0111\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec v\u00e0 m\u1ed9t s\u1ed1 th\u00f4ng tin kh\u00e1c, ta c\u00f3 th\u1ec3 t\u00ednh to\u00e1n t\u1ecda \u0111\u1ed9 c\u1ee7a c\u00e1c \u0111i\u1ec3m E v\u00e0 F l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh AC v\u00e0 AB b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c sau:<\/p>\n<p>T\u1ecda \u0111\u1ed9 x c\u1ee7a E b\u1eb1ng trung b\u00ecnh c\u1ed9ng c\u1ee7a t\u1ecda \u0111\u1ed9 x c\u1ee7a A v\u00e0 C, t\u1ee9c l\u00e0: xE = (x1 + x3) \/ 2.<\/p>\n<p>T\u1ecda \u0111\u1ed9 y c\u1ee7a E b\u1eb1ng trung b\u00ecnh c\u1ed9ng c\u1ee7a t\u1ecda \u0111\u1ed9 y c\u1ee7a A v\u00e0 C, t\u1ee9c l\u00e0: yE = (y1 + y3) \/ 2.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-trung-tuyen-la-gi\/duong-trung-tuyen-la-gi-8\/\" rel=\"attachment wp-att-298693\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-8.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-8-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-8-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298693 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-8.jpg\" alt=\"duong-trung-tuyen-la-gi-8\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-8.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-8-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-8-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>T\u1ecda \u0111\u1ed9 x c\u1ee7a F b\u1eb1ng trung b\u00ecnh c\u1ed9ng c\u1ee7a t\u1ecda \u0111\u1ed9 x c\u1ee7a A v\u00e0 B, t\u1ee9c l\u00e0: xF = (x1 + x2) \/ 2.<\/p>\n<p>T\u1ecda \u0111\u1ed9 y c\u1ee7a F b\u1eb1ng trung b\u00ecnh c\u1ed9ng c\u1ee7a t\u1ecda \u0111\u1ed9 y c\u1ee7a A v\u00e0 B, t\u1ee9c l\u00e0: yF = (y1 + y2) \/ 2.<\/p>\n<p>V\u1eady t\u1ecda \u0111\u1ed9 c\u1ee7a E l\u00e0 E((x1 + x3) \/ 2, (y1 + y3) \/ 2), v\u00e0 t\u1ecda \u0111\u1ed9 c\u1ee7a F l\u00e0 F((x1 + x2) \/ 2, (y1 + y2) \/ 2).<\/p>\n<h2>B\u00e0i t\u1eadp \u00e1p d\u1ee5ng v\u1ec1 \u0111\u01b0\u1eddng trung tuy\u1ebfn<\/h2>\n<p>\u0110\u1ec3 n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c v\u1ec1 \u0111\u01b0\u1eddng trung tuy\u1ebfn v\u00e0 \u00e1p d\u1ee5ng ch\u00fang v\u00e0o th\u1ef1c t\u1ebf, ch\u00fang ta c\u1ea7n th\u1ef1c h\u00e0nh qua c\u00e1c b\u00e0i t\u1eadp. V\u1edbi nh\u1eefng ki\u1ebfn th\u1ee9c v\u1ec1 \u0111\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n c\u1ee7a n\u00f3, sau \u0111\u00e2y ch\u00fang ta s\u1ebd \u00e1p d\u1ee5ng v\u00e0 gi\u1ea3i quy\u1ebft hai b\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn \u0111\u01b0\u1eddng trung tuy\u1ebfn.<\/p>\n<h3>B\u00e0i t\u1eadp s\u1ed1 1: T\u00ednh t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u1ea1nh BC v\u00e0 c\u1ea1nh AC<\/h3>\n<p>Cho tam gi\u00e1c ABC c\u00f3 t\u1ecda \u0111\u1ed9 c\u00e1c \u0111\u1ec9nh l\u00e0 A(1;2), B(3;4) v\u00e0 C(5;6). T\u00ednh t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u1ea1nh BC v\u00e0 c\u1ea1nh AC.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-trung-tuyen-la-gi\/duong-trung-tuyen-la-gi-9\/\" rel=\"attachment wp-att-298694\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-9.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-9-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-9-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298694 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-9.jpg\" alt=\"duong-trung-tuyen-la-gi-9\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-9.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-9-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-9-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>L\u1eddi gi\u1ea3i:<\/p>\n<p>\u0110\u1ec3 t\u00ednh t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u1ea1nh BC, ta l\u1ea5y trung b\u00ecnh c\u1ed9ng c\u1ee7a t\u1ecda \u0111\u1ed9 x v\u00e0 y c\u1ee7a hai \u0111\u1ec9nh B v\u00e0 C. Ta \u0111\u01b0\u1ee3c: M((3+5)\/2; (4+6)\/2) = M(4;5).<\/p>\n<p>\u0110\u1ec3 t\u00ednh t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u1ea1nh AC, ta l\u1ea5y trung b\u00ecnh c\u1ed9ng c\u1ee7a t\u1ecda \u0111\u1ed9 x v\u00e0 y c\u1ee7a hai \u0111\u1ec9nh A v\u00e0 C. Ta \u0111\u01b0\u1ee3c: N((1+5)\/2; (2+6)\/2) = N(3;4)<\/p>\n<p>V\u1eady t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u1ea1nh BC l\u00e0 M(4;5) v\u00e0 t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m ch\u00ednh gi\u1eefa c\u1ea1nh AC l\u00e0 N(3;4).<\/p>\n<h3>B\u00e0i t\u1eadp s\u1ed1 2: T\u00ednh t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh B v\u00e0 \u0111\u1ec9nh C d\u1ef1a tr\u00ean \u0111\u01b0\u1eddng trung tuy\u1ebfn AM<\/h3>\n<p>Cho tam gi\u00e1c ABC c\u00f3 t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh A l\u00e0 A(2;3) v\u00e0 t\u1ecda \u0111\u1ed9 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh BC l\u00e0 M(4;5). Bi\u1ebft r\u1eb1ng \u0111\u01b0\u1eddng trung tuy\u1ebfn AM c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 y = 2x &#8211; 1. T\u00ednh t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh B v\u00e0 \u0111\u1ec9nh C.<\/p>\n<p><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/duong-trung-tuyen-la-gi\/duong-trung-tuyen-la-gi-10\/\" rel=\"attachment wp-att-298695\"><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-10.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-10-300x200.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-10-768x512.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298695 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-10.jpg\" alt=\"duong-trung-tuyen-la-gi-10\" width=\"800\" height=\"533\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-10.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-10-300x200.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/duong-trung-tuyen-la-gi-10-768x512.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/a><\/p>\n<p>L\u1eddi gi\u1ea3i:<\/p>\n<p>\u0110\u1ec3 t\u00ednh t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh B v\u00e0 \u0111\u1ec9nh C, ta c\u1ea7n t\u00ecm ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a c\u1ea1nh BC. Ta c\u00f3 nh\u1eefng th\u00f4ng tin sau:<\/p>\n<ul>\n<li style=\"font-weight: 400;\">C\u1ea1nh BC vu\u00f4ng g\u00f3c v\u1edbi \u0111\u01b0\u1eddng trung tuy\u1ebfn AM, n\u00ean h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a c\u1ea1nh BC l\u00e0 -1\/2 (l\u1ea5y ngh\u1ecbch \u0111\u1ea3o \u0111\u1ed1i c\u1ee7a h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a AM).<\/li>\n<li style=\"font-weight: 400;\">C\u1ea1nh BC \u0111i qua \u0111i\u1ec3m M(4;5), n\u00ean ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a c\u1ea1nh BC c\u00f3 d\u1ea1ng y = -1\/2x + b.<\/li>\n<li style=\"font-weight: 400;\">Thay t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m M v\u00e0o ph\u01b0\u01a1ng tr\u00ecnh, ta \u0111\u01b0\u1ee3c b = 7. V\u1eady ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a c\u1ea1nh BC l\u00e0 y = -1\/2x + 7.<\/li>\n<\/ul>\n<p>B\u00e2y gi\u1edd, ta c\u00f3 th\u1ec3 gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a c\u1ea1nh BC v\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn AM \u0111\u1ec3 t\u00ecm t\u1ecda \u0111\u1ed9 c\u00e1c \u0111\u1ec9nh B v\u00e0 C. Ta c\u00f3 y = -1\/2x + 7 y = 2x &#8211; 1 v\u00e0 ta \u0111\u01b0\u1ee3c x = 2 v\u00e0 y = 3. Do \u0111\u00f3, t\u1ecda \u0111\u1ed9 c\u1ee7a \u0111\u1ec9nh B ho\u1eb7c \u0111\u1ec9nh C l\u00e0 (2;3).<\/p>\n<p>\u0110\u1ec3 t\u00ecm t\u1ecda \u0111\u1ed9 c\u1ee7a \u0111\u1ec9nh c\u00f2n l\u1ea1i, ta d\u00f9ng t\u00ednh ch\u1ea5t c\u1ee7a \u0111i\u1ec3m trung \u0111i\u1ec3m. Ta c\u00f3: M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a BC, n\u00ean t\u1ecda \u0111\u1ed9 x v\u00e0 y c\u1ee7a M b\u1eb1ng trung b\u00ecnh c\u1ed9ng c\u1ee7a t\u1ecda \u0111\u1ed9 x v\u00e0 y c\u1ee7a B v\u00e0 C. T\u1eeb \u0111\u00f3 suy ra 4 = (2 + x)\/2 5 = (3 + y)\/2<\/p>\n<p>Gi\u1ea3i h\u1ec7, ta \u0111\u01b0\u1ee3c x = 6 v\u00e0 y = 7 l\u00e0 t\u1ecda \u0111\u1ed9 c\u1ee7a \u0111\u1ec9nh c\u00f2n l\u1ea1i. V\u1eady t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh B l\u00e0 (2;3) v\u00e0 t\u1ecda \u0111\u1ed9 \u0111\u1ec9nh C l\u00e0 (6;7) ho\u1eb7c ng\u01b0\u1ee3c l\u1ea1i.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>Qua b\u00e0i vi\u1ebft n\u00e0y, ch\u00fang ta \u0111\u00e3 n\u1eafm \u0111\u01b0\u1ee3c <strong>\u0111\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec<\/strong> v\u00e0 m\u1ed9t s\u1ed1 th\u00f4ng tin chi ti\u1ebft kh\u00e1c v\u1ec1 \u0111o\u1ea1n th\u1eb3ng n\u00e0y. \u0110\u1ec3 n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c v\u1ec1 \u0111\u01b0\u1eddng trung tuy\u1ebfn, ch\u00fang ta c\u1ea7n \u00f4n t\u1eadp v\u00e0 luy\u1ec7n t\u1eadp th\u01b0\u1eddng xuy\u00ean c\u00e1c b\u00e0i t\u1eadp v\u1ec1 \u0111\u01b0\u1eddng th\u1eb3ng n\u00e0y, \u0111\u1eb7c bi\u1ec7t l\u00e0 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp th\u01b0\u1eddng g\u1eb7p. Hy v\u1ecdng b\u00e0i vi\u1ebft n\u00e0y s\u1ebd gi\u00fap \u00edch cho c\u00e1c b\u1ea1n trong vi\u1ec7c h\u1ecdc t\u1eadp v\u00e0 n\u00e2ng cao k\u1ef9 n\u0103ng gi\u1ea3i to\u00e1n v\u1ec1 h\u00ecnh h\u1ecdc.<\/p>\n<p>Xem th\u00eam:<\/p>\n<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-hinh-vuong\/\">C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng ch\u00ednh x\u00e1c nh\u1ea5t<\/a><\/p>\n<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/so-thuc-la-gi\/\">S\u1ed1 th\u1ef1c l\u00e0 g\u00ec? M\u1ed9t s\u1ed1 d\u1ea1ng to\u00e1n h\u1ecdc ph\u1ed5 bi\u1ebfn v\u1ec1 s\u1ed1 th\u1ef1c<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m ph\u1ed5 bi\u1ebfn trong h\u00ecnh h\u1ecdc kh\u00f4ng gian v\u00e0 ch\u1ee7 y\u1ebfu \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng trong tam gi\u00e1c. V\u1edbi nh\u1eefng ki\u1ebfn th\u1ee9c v\u1ec1 kh\u00e1i ni\u1ec7m v\u00e0 c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n, ch\u00fang ta c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng ch\u00fang \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc li\u00ean quan \u0111\u1ebfn tam gi\u00e1c [&hellip;]<\/p>\n","protected":false},"author":86,"featured_media":298686,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-298566","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v24.2 (Yoast SEO v24.2) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0110\u01b0\u1eddng trung tuy\u1ebfn l\u00e0 g\u00ec? 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