{"id":374436,"date":"2024-08-13T20:36:19","date_gmt":"2024-08-13T13:36:19","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=374436"},"modified":"2024-08-13T20:36:19","modified_gmt":"2024-08-13T13:36:19","slug":"tia-phan-giac-la-gi","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/tia-phan-giac-la-gi\/","title":{"rendered":"Tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? T\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c"},"content":{"rendered":"<p>Trong h\u00ecnh h\u1ecdc, <strong>tia ph\u00e2n gi\u00e1c<\/strong> l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng v\u00e0 quen thu\u1ed9c, \u0111\u1eb7c bi\u1ec7t l\u00e0 trong vi\u1ec7c gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n v\u1ec1 tam gi\u00e1c. V\u1eady <strong>tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec<\/strong> v\u00e0 l\u00e0m th\u1ebf n\u00e0o \u0111\u1ec3 nh\u1eadn bi\u1ebft c\u0169ng nh\u01b0 \u00e1p d\u1ee5ng trong th\u1ef1c t\u1ebf? B\u00e0i vi\u1ebft n\u00e0y s\u1ebd gi\u1ea3i \u0111\u00e1p nh\u1eefng th\u1eafc m\u1eafc \u0111\u00f3 v\u00e0 \u0111i s\u00e2u v\u00e0o vi\u1ec7c kh\u00e1m ph\u00e1 <strong>\u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c<\/strong> c\u00f9ng v\u1edbi nh\u1eefng t\u00ednh ch\u1ea5t \u0111\u1eb7c bi\u1ec7t c\u1ee7a n\u00f3 trong tam gi\u00e1c. H\u00e3y c\u00f9ng t\u00ecm hi\u1ec3u \u0111\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 vai tr\u00f2 c\u1ee7a tia ph\u00e2n gi\u00e1c trong vi\u1ec7c chia g\u00f3c v\u00e0 c\u00e1ch n\u00f3 gi\u00fap \u0111\u01a1n gi\u1ea3n h\u00f3a nh\u1eefng b\u00e0i to\u00e1n ph\u1ee9c t\u1ea1p!<\/p>\n<h2>Tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec<\/h2>\n<p>Trong h\u00ecnh h\u1ecdc, tia ph\u00e2n gi\u00e1c l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n nh\u01b0ng v\u00f4 c\u00f9ng quan tr\u1ecdng, \u0111\u1eb7c bi\u1ec7t khi l\u00e0m vi\u1ec7c v\u1edbi c\u00e1c b\u00e0i to\u00e1n v\u1ec1 g\u00f3c v\u00e0 tam gi\u00e1c. Tia ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c l\u00e0 m\u1ed9t tia b\u1eaft \u0111\u1ea7u t\u1eeb \u0111\u1ec9nh c\u1ee7a g\u00f3c v\u00e0 chia g\u00f3c \u0111\u00f3 th\u00e0nh hai ph\u1ea7n c\u00f3 \u0111\u1ed9 l\u1edbn b\u1eb1ng nhau. Ngh\u0129a l\u00e0, n\u1ebfu b\u1ea1n c\u00f3 m\u1ed9t g\u00f3c tam gi\u00e1c ABC, tia ph\u00e2n gi\u00e1c s\u1ebd xu\u1ea5t ph\u00e1t t\u1eeb \u0111\u1ec9nh B v\u00e0 \u0111i qua m\u1ed9t \u0111i\u1ec3m D n\u00e0o \u0111\u00f3 tr\u00ean c\u1ea1nh c\u1ee7a g\u00f3c, t\u1ea1o th\u00e0nh hai g\u00f3c ABD v\u00e0 DBC c\u00f3 k\u00edch th\u01b0\u1edbc b\u1eb1ng nhau.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-2-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-2-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-374530 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-2.jpg\" alt=\"tia-phan-giac-la-gi-\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>T\u00ednh ch\u1ea5t c\u1ee7a tia ph\u00e2n gi\u00e1c<\/strong><\/p>\n<ul>\n<li>\u0110\u1ed9 ch\u00ednh x\u00e1c: Tia ph\u00e2n gi\u00e1c chia g\u00f3c ban \u0111\u1ea7u th\u00e0nh hai g\u00f3c b\u1eb1ng nhau m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c, \u0111i\u1ec1u n\u00e0y r\u1ea5t h\u1eefu \u00edch trong vi\u1ec7c t\u00ednh to\u00e1n v\u00e0 v\u1ebd h\u00ecnh.<\/li>\n<li>Vai tr\u00f2 trong tam gi\u00e1c: Trong m\u1ed9t tam gi\u00e1c, ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c (n\u1ed1i t\u1eeb c\u00e1c \u0111\u1ec9nh t\u1edbi ph\u00eda \u0111\u1ed1i di\u1ec7n) lu\u00f4n c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m \u0111\u1eb7c bi\u1ec7t g\u1ecdi l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp. \u0110\u00e2y l\u00e0 \u0111i\u1ec3m m\u00e0 t\u1eeb \u0111\u00f3 c\u00f3 th\u1ec3 v\u1ebd m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n ti\u1ebfp x\u00fac v\u1edbi t\u1ea5t c\u1ea3 c\u00e1c c\u1ea1nh tam gi\u00e1c.<\/li>\n<\/ul>\n<h2>C\u00e1ch nh\u1eadn bi\u1ebft v\u00e0 v\u1ebd tia ph\u00e2n gi\u00e1c<\/h2>\n<p>Nh\u01b0 v\u1eady, b\u1ea1n \u0111\u00e3 bi\u1ebft tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec. Tia ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c l\u00e0 m\u1ed9t tia b\u1eaft \u0111\u1ea7u t\u1eeb \u0111\u1ec9nh c\u1ee7a g\u00f3c v\u00e0 chia g\u00f3c \u0111\u00f3 th\u00e0nh hai ph\u1ea7n c\u00f3 k\u00edch th\u01b0\u1edbc b\u1eb1ng nhau.<\/p>\n<p>Tia ph\u00e2n gi\u00e1c t\u1ea1o ra hai g\u00f3c con b\u1eb1ng nhau, \u0111i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 n\u1ebfu b\u1ea1n c\u00f3 g\u00f3c \u2220ABC, tia ph\u00e2n gi\u00e1c s\u1ebd chia g\u00f3c n\u00e0y th\u00e0nh hai g\u00f3c con \u2220ABD v\u00e0 \u2220DBC sao cho: \u2220ABD=\u2220DBC.<\/p>\n<p><strong>C\u00e1ch v\u1ebd tia ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c:<\/strong><\/p>\n<p><strong>B\u01b0\u1edbc 1:<\/strong> V\u1ebd m\u1ed9t g\u00f3c. \u0110\u1eb7t \u0111i\u1ec3m B l\u00e0m \u0111\u1ec9nh c\u1ee7a g\u00f3c v\u00e0 v\u1ebd hai c\u1ea1nh c\u1ee7a g\u00f3c, v\u00ed d\u1ee5 nh\u01b0 BA v\u00e0 BC.<\/p>\n<p><strong>B\u01b0\u1edbc 2:<\/strong> S\u1eed d\u1ee5ng m\u1ed9t d\u1ee5ng c\u1ee5 \u0111o g\u00f3c (th\u01b0\u1edbc \u0111o g\u00f3c) ho\u1eb7c ph\u1ea7n m\u1ec1m v\u1ebd h\u00ecnh h\u1ecdc \u0111\u1ec3 \u0111o k\u00edch th\u01b0\u1edbc c\u1ee7a g\u00f3c \u2220ABC. Ghi nh\u1edb k\u00edch th\u01b0\u1edbc n\u00e0y ho\u1eb7c l\u01b0u n\u00f3 \u0111\u1ec3 so s\u00e1nh sau.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-3-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-3-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-374529 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-3.jpg\" alt=\"tia-phan-giac-la-gi-\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>B\u01b0\u1edbc 3:<\/strong> X\u00e1c \u0111\u1ecbnh \u0111i\u1ec3m ph\u00e2n gi\u00e1c. \u0110\u1eb7t th\u01b0\u1edbc k\u1ebb ho\u1eb7c ph\u1ea7n m\u1ec1m v\u1ebd h\u00ecnh h\u1ecdc sao cho n\u00f3 chia g\u00f3c \u2220ABC th\u00e0nh hai g\u00f3c b\u1eb1ng nhau. \u0110o v\u00e0 \u0111\u00e1nh d\u1ea5u \u0111i\u1ec3m tr\u00ean c\u1ea1nh c\u1ee7a g\u00f3c sao cho hai ph\u1ea7n c\u1ee7a g\u00f3c c\u00f3 k\u00edch th\u01b0\u1edbc b\u1eb1ng nhau.<\/p>\n<p><strong>B\u01b0\u1edbc 4:<\/strong> V\u1ebd tia t\u1eeb \u0111\u1ec9nh c\u1ee7a g\u00f3c qua \u0111i\u1ec3m b\u1ea1n \u0111\u00e3 \u0111\u00e1nh d\u1ea5u. Tia n\u00e0y ch\u00ednh l\u00e0 tia ph\u00e2n gi\u00e1c, chia g\u00f3c \u2220ABC th\u00e0nh hai g\u00f3c con b\u1eb1ng nhau.<\/p>\n<p><strong>B\u01b0\u1edbc 5:<\/strong> Ki\u1ec3m tra l\u1ea1i. \u0110\u1ea3m b\u1ea3o r\u1eb1ng hai g\u00f3c con \u0111\u01b0\u1ee3c t\u1ea1o ra b\u1edfi tia ph\u00e2n gi\u00e1c l\u00e0 b\u1eb1ng nhau b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng th\u01b0\u1edbc \u0111o g\u00f3c m\u1ed9t l\u1ea7n n\u1eefa.<\/p>\n<h2>\u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c l\u00e0 g\u00ec<\/h2>\n<p>Ngo\u00e0i vi\u1ec7c c\u1ea7n t\u00ecm hi\u1ec3u tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec, ch\u00fang ta c\u0169ng c\u1ea7n hi\u1ec3u \u0111\u01b0\u1ee3c kh\u00e1i ni\u1ec7m \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong m\u1ed9t tam gi\u00e1c. \u0110\u00f3 l\u00e0 m\u1ed9t \u0111o\u1ea1n th\u1eb3ng n\u1ed1i t\u1eeb m\u1ed9t \u0111\u1ec9nh tam gi\u00e1c \u0111\u1ebfn \u0111i\u1ec3m c\u1eaft c\u1ee7a ph\u00e2n gi\u00e1c \u0111\u00f3 v\u1edbi c\u1ea1nh \u0111\u1ed1i di\u1ec7n tam gi\u00e1c.<\/p>\n<p>\u0110\u1eb7c bi\u1ec7t, \u0111\u01b0\u1eddng\/tia ph\u00e2n gi\u00e1c chia g\u00f3c t\u1ea1i \u0111\u1ec9nh tam gi\u00e1c th\u00e0nh hai g\u00f3c c\u00f3 k\u00edch th\u01b0\u1edbc b\u1eb1ng nhau. \u0110o\u1ea1n th\u1eb3ng n\u00e0y kh\u00f4ng ch\u1ec9 chia g\u00f3c th\u00e0nh hai ph\u1ea7n b\u1eb1ng nhau m\u00e0 c\u00f2n chia c\u1ea1nh \u0111\u1ed1i di\u1ec7n tam gi\u00e1c th\u00e0nh hai ph\u1ea7n t\u1ec9 l\u1ec7 v\u1edbi c\u00e1c c\u1ea1nh c\u00f2n l\u1ea1i c\u1ee7a tam gi\u00e1c.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-4-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-4-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-374528 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-4.jpg\" alt=\"tia-phan-giac-la-gi-\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>\u0110\u1ecbnh Ngh\u0129a:<\/strong> \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a m\u1ed9t tam gi\u00e1c l\u00e0 \u0111o\u1ea1n th\u1eb3ng xu\u1ea5t ph\u00e1t t\u1eeb m\u1ed9t \u0111\u1ec9nh v\u00e0 chia g\u00f3c t\u1ea1i \u0111\u1ec9nh \u0111\u00f3 th\u00e0nh hai g\u00f3c b\u1eb1ng nhau. \u0110\u1ed3ng th\u1eddi, n\u00f3 c\u1eaft c\u1ea1nh \u0111\u1ed1i di\u1ec7n t\u1ea1i \u0111i\u1ec3m m\u00e0 t\u1eeb \u0111\u00f3, t\u1ef7 l\u1ec7 gi\u1eefa c\u00e1c \u0111o\u1ea1n c\u1ee7a c\u1ea1nh \u0111\u1ed1i di\u1ec7n b\u1eb1ng t\u1ef7 l\u1ec7 gi\u1eefa c\u00e1c c\u1ea1nh c\u00f2n l\u1ea1i c\u1ee7a tam gi\u00e1c.<\/p>\n<p>\u0110o\u00e1n v\u00e0 v\u1ebd m\u1ed9t \u0111o\u1ea1n th\u1eb3ng t\u1eeb \u0111\u1ec9nh c\u1ee7a g\u00f3c \u0111\u1ebfn c\u1ea1nh \u0111\u1ed1i di\u1ec7n sao cho n\u00f3 chia g\u00f3c th\u00e0nh hai g\u00f3c b\u1eb1ng nhau. Ki\u1ec3m tra t\u1ef7 l\u1ec7 c\u1ee7a c\u00e1c \u0111o\u1ea1n tr\u00ean c\u1ea1nh \u0111\u1ed1i di\u1ec7n \u0111\u1ec3 x\u00e1c nh\u1eadn r\u1eb1ng ch\u00fang \u0111\u00fang theo t\u1ef7 l\u1ec7 c\u1ee7a c\u00e1c c\u1ea1nh c\u00f2n l\u1ea1i t\u1ea1i tam gi\u00e1c.<\/p>\n<h2>T\u00ednh ch\u1ea5t ch\u00ednh c\u1ee7a \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c<\/h2>\n<p><strong>Chia G\u00f3c Th\u00e0nh Hai Ph\u1ea7n B\u1eb1ng Nhau: <\/strong>T\u00ednh ch\u1ea5t n\u1ed5i b\u1eadt nh\u1ea5t c\u1ee7a tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? L\u00e0 kh\u1ea3 n\u0103ng chia g\u00f3c t\u1ea1i \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c th\u00e0nh hai g\u00f3c c\u00f3 k\u00edch th\u01b0\u1edbc b\u1eb1ng nhau. Khi b\u1ea1n bi\u1ebft v\u1ec1 tia ph\u00e2n gi\u00e1c v\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c, b\u1ea1n c\u00f3 th\u1ec3 d\u1ec5 d\u00e0ng ch\u1ee9ng minh r\u1eb1ng c\u00e1c g\u00f3c con do tia ph\u00e2n gi\u00e1c t\u1ea1o ra l\u00e0 b\u1eb1ng nhau, t\u1eeb \u0111\u00f3 gi\u00fap x\u00e1c \u0111\u1ecbnh v\u00e0 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn g\u00f3c trong tam gi\u00e1c.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-1.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-1-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-1-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-374531 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-1.jpg\" alt=\"tia-phan-giac-la-gi-\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>T\u00ednh T\u1ef7 L\u1ec7 C\u1ea1nh \u0110\u1ed1i Di\u1ec7n:<\/strong> \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c chia c\u1ea1nh \u0111\u1ed1i di\u1ec7n tam gi\u00e1c th\u00e0nh hai \u0111o\u1ea1n c\u00f3 t\u1ef7 l\u1ec7 b\u1eb1ng v\u1edbi c\u00e1c c\u1ea1nh c\u00f2n l\u1ea1i c\u1ee7a tam gi\u00e1c. C\u1ee5 th\u1ec3, n\u1ebfu \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1eaft c\u1ea1nh \u0111\u1ed1i di\u1ec7n t\u1ea1i \u0111i\u1ec3m D, th\u00ec t\u1ef7 l\u1ec7 c\u1ee7a c\u00e1c \u0111o\u1ea1n BD v\u00e0 DC b\u1eb1ng t\u1ef7 l\u1ec7 c\u1ee7a c\u00e1c c\u1ea1nh c\u00f2n l\u1ea1i c\u1ee7a tam gi\u00e1c. \u0110i\u1ec1u n\u00e0y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u th\u1ecb b\u1eb1ng c\u00f4ng th\u1ee9c: AC\/AB = DC\/BD.<\/p>\n<p><strong>\u0110i\u1ec3m Giao Nhau C\u1ee7a C\u00e1c \u0110\u01b0\u1eddng Ph\u00e2n Gi\u00e1c:<\/strong> Trong m\u1ed9t tam gi\u00e1c, ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m \u0111\u1eb7c bi\u1ec7t g\u1ecdi l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp. T\u00e2m n\u00e0y l\u00e0 \u0111i\u1ec3m t\u1eeb \u0111\u00f3 b\u1ea1n c\u00f3 th\u1ec3 v\u1ebd m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n ti\u1ebfp x\u00fac v\u1edbi t\u1ea5t c\u1ea3 c\u00e1c c\u1ea1nh tam gi\u00e1c.<\/p>\n<h2>\u1ee8ng d\u1ee5ng t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c<\/h2>\n<p><strong>Ch\u1ee9ng Minh \u0110\u1ecbnh L\u00fd<\/strong>: T\u00ednh ch\u1ea5t c\u1ee7a \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c d\u00f9ng \u0111\u1ec3 ch\u1ee9ng minh nhi\u1ec1u \u0111\u1ecbnh l\u00fd trong h\u00ecnh h\u1ecdc, ch\u1eb3ng h\u1ea1n nh\u01b0 \u0111\u1ecbnh l\u00fd v\u1ec1 t\u1ef7 l\u1ec7 ph\u00e2n chia c\u1ea1nh \u0111\u1ed1i di\u1ec7n v\u00e0 c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn c\u00e1c g\u00f3c trong tam gi\u00e1c.<\/p>\n<p><strong>Gi\u1ea3i Quy\u1ebft B\u00e0i To\u00e1n<\/strong>: Trong c\u00e1c b\u00e0i to\u00e1n v\u1ec1 tam gi\u00e1c, \u0111\u1eb7c bi\u1ec7t l\u00e0 khi c\u1ea7n t\u00ednh to\u00e1n t\u1ef7 l\u1ec7 c\u00e1c \u0111o\u1ea1n v\u00e0 c\u00e1c g\u00f3c, vi\u1ec7c hi\u1ec3u r\u00f5 t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c gi\u00fap b\u1ea1n gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c v\u00e0 hi\u1ec7u qu\u1ea3.<\/p>\n<p><strong>Thi\u1ebft K\u1ebf Ki\u1ebfn Tr\u00fac<\/strong>: Hi\u1ec3u \u0111\u01b0\u1ee3c t\u00ednh ch\u1ea5t c\u1ee7a tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec c\u0169ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng trong thi\u1ebft k\u1ebf ki\u1ebfn tr\u00fac \u0111\u1ec3 t\u1ea1o ra c\u00e1c c\u1ea5u tr\u00fac \u0111\u1ed1i x\u1ee9ng v\u00e0 c\u00e2n \u0111\u1ed1i.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi--300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi--768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-374532 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-.jpg\" alt=\"tia-phan-giac-la-gi-\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi--300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi--768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>V\u00ed d\u1ee5 minh h\u1ecda: <\/strong>H\u00e3y xem x\u00e9t m\u1ed9t tam gi\u00e1c ABC v\u1edbi \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c AD. \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c AD chia g\u00f3c \u2220BAC th\u00e0nh hai g\u00f3c b\u1eb1ng nhau v\u00e0 chia c\u1ea1nh \u0111\u1ed1i di\u1ec7n BC th\u00e0nh hai \u0111o\u1ea1n BD v\u00e0 DC theo t\u1ef7 l\u1ec7: <strong>AC\/AB = DC\/BD.<\/strong><\/p>\n<p>\u0110i\u1ec1u n\u00e0y ch\u1ee9ng minh r\u1eb1ng c\u00e1c \u0111o\u1ea1n BD v\u00e0 DC chia c\u1ea1nh BC theo t\u1ef7 l\u1ec7 c\u1ee7a c\u00e1c c\u1ea1nh AB v\u00e0 AC, cho ph\u00e9p b\u1ea1n t\u00ednh to\u00e1n c\u00e1c \u0111\u1ed9 d\u00e0i v\u00e0 g\u00f3c m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c.<\/p>\n<h2>S\u1ef1 kh\u00e1c bi\u1ec7t gi\u1eefa tia ph\u00e2n gi\u00e1c v\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c<\/h2>\n<p>Tia ph\u00e2n gi\u00e1c v\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c th\u01b0\u1eddng b\u1ecb nh\u1ea7m l\u1eabn, nh\u01b0ng ch\u00fang c\u00f3 s\u1ef1 kh\u00e1c bi\u1ec7t r\u00f5 r\u00e0ng:<\/p>\n<p><strong>Tia Ph\u00e2n Gi\u00e1c:<\/strong> L\u00e0 m\u1ed9t tia b\u1eaft \u0111\u1ea7u t\u1eeb \u0111\u1ec9nh c\u1ee7a m\u1ed9t g\u00f3c v\u00e0 chia g\u00f3c \u0111\u00f3 th\u00e0nh hai g\u00f3c b\u1eb1ng nhau. Tia ph\u00e2n gi\u00e1c kh\u00f4ng ph\u1ea3i l\u00e0 \u0111o\u1ea1n th\u1eb3ng c\u00f3 \u0111\u1ed9 d\u00e0i x\u00e1c \u0111\u1ecbnh m\u00e0 l\u00e0 m\u1ed9t ph\u1ea7n c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u00f4 h\u1ea1n.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-6.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-6-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-6-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-374533 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-6.jpg\" alt=\"tia-phan-giac-la-gi-\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>\u0110\u01b0\u1eddng Ph\u00e2n Gi\u00e1c:<\/strong> Trong m\u1ed9t tam gi\u00e1c, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c l\u00e0 \u0111o\u1ea1n th\u1eb3ng n\u1ed1i t\u1eeb m\u1ed9t \u0111\u1ec9nh tam gi\u00e1c \u0111\u1ebfn \u0111i\u1ec3m c\u1eaft c\u1ee7a tia ph\u00e2n gi\u00e1c v\u1edbi c\u1ea1nh \u0111\u1ed1i di\u1ec7n. \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c l\u00e0 m\u1ed9t \u0111o\u1ea1n th\u1eb3ng c\u00f3 \u0111\u1ed9 d\u00e0i x\u00e1c \u0111\u1ecbnh v\u00e0 chia c\u1ea1nh \u0111\u1ed1i di\u1ec7n tam gi\u00e1c theo t\u1ef7 l\u1ec7 nh\u1ea5t \u0111\u1ecbnh.<\/p>\n<p><strong>M\u1ed1i Quan H\u1ec7:<\/strong> Tia ph\u00e2n gi\u00e1c l\u00e0 th\u00e0nh ph\u1ea7n c\u01a1 b\u1ea3n c\u00f3 th\u1ec3 d\u1ef1a v\u00e0o t\u1eeb \u0111\u00f3 x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c. \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c ch\u00ednh l\u00e0 \u0111o\u1ea1n th\u1eb3ng m\u00e0 tia ph\u00e2n gi\u00e1c c\u1eaft c\u1ea1nh \u0111\u1ed1i di\u1ec7n tam gi\u00e1c, v\u00e0 n\u00f3 chia c\u1ea1nh \u0111\u1ed1i di\u1ec7n th\u00e0nh hai ph\u1ea7n t\u01b0\u01a1ng \u1ee9ng.<\/p>\n<h2>\u1ee8ng d\u1ee5ng c\u1ee7a tia ph\u00e2n gi\u00e1c<\/h2>\n<p>Tia ph\u00e2n gi\u00e1c kh\u00f4ng ch\u1ec9 l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n trong h\u00ecnh h\u1ecdc m\u00e0 c\u00f2n c\u00f3 r\u1ea5t nhi\u1ec1u \u1ee9ng d\u1ee5ng th\u1ef1c ti\u1ec5n trong to\u00e1n h\u1ecdc v\u00e0 c\u00e1c l\u0129nh v\u1ef1c c\u1ee7a \u0111\u1eddi s\u1ed1ng. V\u1eady \u1ee9ng d\u1ee5ng c\u1ee7a tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? H\u00e3y c\u00f9ng kh\u00e1m ph\u00e1 m\u1ed9t s\u1ed1 \u1ee9ng d\u1ee5ng quan tr\u1ecdng d\u01b0\u1edbi \u0111\u00e2y.<\/p>\n<h3>\u1ee8ng d\u1ee5ng gi\u1ea3i to\u00e1n h\u00ecnh h\u1ecdc c\u1ee7a tia ph\u00e2n gi\u00e1c<\/h3>\n<p>Trong to\u00e1n h\u1ecdc, \u0111\u1eb7c bi\u1ec7t l\u00e0 h\u00ecnh h\u1ecdc, d\u00f9ng tia ph\u00e2n gi\u00e1c c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn g\u00f3c v\u00e0 tam gi\u00e1c.<\/p>\n<p><strong>Ch\u1ee9ng minh t\u00ednh ch\u1ea5t g\u00f3c:<\/strong> Tia ph\u00e2n gi\u00e1c \u0111\u01b0\u1ee3c d\u00f9ng \u0111\u1ec3 ch\u1ee9ng minh hai g\u00f3c b\u1eb1ng nhau ho\u1eb7c \u0111\u1ec3 t\u00ecm ra c\u00e1c g\u00f3c trong c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc ph\u1ee9c t\u1ea1p. V\u00ed d\u1ee5, trong tam gi\u00e1c, n\u1ebfu m\u1ed9t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c chia m\u1ed9t g\u00f3c th\u00e0nh hai ph\u1ea7n b\u1eb1ng nhau, n\u00f3 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ch\u1ee9ng minh r\u1eb1ng hai \u0111o\u1ea1n th\u1eb3ng \u0111\u1ed1i di\u1ec7n c\u0169ng c\u00f3 t\u1ec9 l\u1ec7 nh\u1ea5t \u0111\u1ecbnh, th\u00f4ng qua \u0111\u1ecbnh l\u00fd \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-5.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-5-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-5-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-374534 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-5.jpg\" alt=\"tia-phan-giac-la-gi-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>X\u00e1c \u0111\u1ecbnh t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp:<\/strong> Trong m\u1ed9t tam gi\u00e1c, ba tia ph\u00e2n gi\u00e1c c\u1ee7a ba g\u00f3c s\u1ebd c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m g\u1ecdi l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp. \u0110i\u1ec3m n\u00e0y r\u1ea5t quan tr\u1ecdng c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh v\u1ecb tr\u00ed v\u00e0 k\u00edch th\u01b0\u1edbc c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp tam gi\u00e1c, gi\u00fap t\u00ednh to\u00e1n d\u1ec5 d\u00e0ng h\u01a1n trong c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn di\u1ec7n t\u00edch v\u00e0 chu vi.<\/p>\n<p><strong>Gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n \u0111\u1ed1i x\u1ee9ng:<\/strong> Tia ph\u00e2n gi\u00e1c th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u1ea1o ra c\u00e1c b\u00e0i to\u00e1n v\u1ec1 \u0111\u1ed1i x\u1ee9ng trong h\u00ecnh h\u1ecdc.<\/p>\n<h3>\u1ee8ng d\u1ee5ng trong ki\u1ebfn tr\u00fac v\u00e0 k\u1ef9 thu\u1eadt c\u1ee7a tia ph\u00e2n gi\u00e1c<\/h3>\n<p>Ngo\u00e0i to\u00e1n h\u1ecdc, tia ph\u00e2n gi\u00e1c c\u0169ng c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng trong ki\u1ebfn tr\u00fac v\u00e0 k\u1ef9 thu\u1eadt:<\/p>\n<p><strong>Thi\u1ebft k\u1ebf ki\u1ebfn tr\u00fac:<\/strong> Tia ph\u00e2n gi\u00e1c \u0111\u01b0\u1ee3c d\u00f9ng trong thi\u1ebft k\u1ebf ki\u1ebfn tr\u00fac \u0111\u1ec3 t\u1ea1o ra nh\u1eefng c\u1ea5u tr\u00fac \u0111\u1ed1i x\u1ee9ng v\u00e0 c\u00e2n \u0111\u1ed1i. Vi\u1ec7c \u00e1p d\u1ee5ng tia ph\u00e2n gi\u00e1c gi\u00fap ki\u1ebfn tr\u00fac s\u01b0 \u0111\u1ea3m b\u1ea3o c\u00e1c g\u00f3c v\u00e0 c\u1ea1nh \u0111\u01b0\u1ee3c ph\u00e2n chia m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c, t\u1eeb \u0111\u00f3 t\u1ea1o ra c\u00e1c c\u00f4ng tr\u00ecnh h\u00e0i h\u00f2a v\u1ec1 m\u1eb7t th\u1ea9m m\u1ef9.<\/p>\n<p><strong>K\u1ef9 thu\u1eadt c\u01a1 kh\u00ed:<\/strong> Trong k\u1ef9 thu\u1eadt c\u01a1 kh\u00ed, \u1ee9ng d\u1ee5ng tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? Tia ph\u00e2n gi\u00e1c c\u00f3 th\u1ec3 d\u00f9ng \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o \u0111\u1ed9 ch\u00ednh x\u00e1c trong vi\u1ec7c l\u1eafp r\u00e1p c\u00e1c b\u1ed9 ph\u1eadn m\u00e1y m\u00f3c. \u0110i\u1ec1u n\u00e0y gi\u00fap c\u1ea3i thi\u1ec7n hi\u1ec7u su\u1ea5t v\u00e0 \u0111\u1ed9 b\u1ec1n c\u1ee7a c\u00e1c thi\u1ebft b\u1ecb c\u01a1 kh\u00ed.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-7.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-7-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-7-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-374535 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-7.jpg\" alt=\"tia-phan-giac-la-gi-7\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-7-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-7-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>Thi\u1ebft k\u1ebf s\u1ea3n ph\u1ea9m:<\/strong> Trong thi\u1ebft k\u1ebf s\u1ea3n ph\u1ea9m, tia ph\u00e2n gi\u00e1c gi\u00fap c\u00e1c nh\u00e0 thi\u1ebft k\u1ebf t\u1ea1o ra c\u00e1c s\u1ea3n ph\u1ea9m c\u00f3 t\u00ednh th\u1ea9m m\u1ef9 v\u00e0 ch\u1ee9c n\u0103ng t\u1ed1t h\u01a1n, \u0111\u1eb7c bi\u1ec7t l\u00e0 trong vi\u1ec7c ph\u00e2n chia kh\u00f4ng gian ho\u1eb7c t\u1ea1o ra c\u00e1c g\u00f3c c\u00e2n \u0111\u1ed1i.<\/p>\n<h3>\u1ee8ng d\u1ee5ng trong \u0111\u1eddi s\u1ed1ng c\u1ee7a tia ph\u00e2n gi\u00e1c<\/h3>\n<p>Tia ph\u00e2n gi\u00e1c c\u0169ng xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u t\u00ecnh hu\u1ed1ng h\u00e0ng ng\u00e0y m\u00e0 ch\u00fang ta c\u00f3 th\u1ec3 kh\u00f4ng \u0111\u1ec3 \u00fd:<\/p>\n<p><strong>Trang tr\u00ed n\u1ed9i th\u1ea5t:<\/strong> Trong trang tr\u00ed n\u1ed9i th\u1ea5t, \u1ee9ng d\u1ee5ng tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? Tia n\u00e0y gi\u00fap t\u1ea1o ra c\u00e1c kh\u00f4ng gian c\u00e2n \u0111\u1ed1i v\u00e0 h\u00e0i h\u00f2a. \u0110i\u1ec1u n\u00e0y c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c th\u1ea5y r\u00f5 trong vi\u1ec7c b\u1ed1 tr\u00ed \u0111\u1ed3 n\u1ed9i th\u1ea5t sao cho kh\u00f4ng gian s\u1ed1ng tr\u1edf n\u00ean tho\u1ea3i m\u00e1i v\u00e0 \u0111\u1eb9p m\u1eaft h\u01a1n.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-8.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-8-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2024\/08\/tia-phan-giac-la-gi-8-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-374536 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-8.jpg\" alt=\"tia-phan-giac-la-gi-\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-8.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-8-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-8-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>Thi\u1ebft k\u1ebf \u0111\u1ed3 h\u1ecda:<\/strong> Tia ph\u00e2n gi\u00e1c d\u00f9ng trong thi\u1ebft k\u1ebf \u0111\u1ed3 h\u1ecda \u0111\u1ec3 t\u1ea1o ra c\u00e1c t\u00e1c ph\u1ea9m ngh\u1ec7 thu\u1eadt \u0111\u1ed1i x\u1ee9ng v\u00e0 c\u00e2n \u0111\u1ed1i, t\u1eeb logo \u0111\u1ebfn poster.<\/p>\n<p><strong>Gi\u00e1o d\u1ee5c:<\/strong> Trong gi\u1ea3ng d\u1ea1y to\u00e1n h\u1ecdc, tia ph\u00e2n gi\u00e1c c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng nh\u01b0 m\u1ed9t c\u00f4ng c\u1ee5 \u0111\u1ec3 gi\u1ea3ng gi\u1ea3i c\u00e1c kh\u00e1i ni\u1ec7m h\u00ecnh h\u1ecdc cho h\u1ecdc sinh, gi\u00fap h\u1ecd hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u00e1c nguy\u00ean l\u00fd v\u00e0 \u0111\u1ecbnh l\u00fd trong to\u00e1n h\u1ecdc.<\/p>\n<h2>FAQ &#8211; C\u00e1c c\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 tia ph\u00e2n gi\u00e1c<\/h2>\n<p><strong>L\u00e0m th\u1ebf n\u00e0o \u0111\u1ec3 ki\u1ec3m tra \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u00f3 ch\u00ednh x\u00e1c kh\u00f4ng?<\/strong><\/p>\n<p>\u0110\u1ec3 ki\u1ec3m tra \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c, b\u1ea1n c\u00f3 th\u1ec3:<\/p>\n<ul>\n<li>S\u1eed d\u1ee5ng d\u1ee5ng c\u1ee5 \u0111o g\u00f3c \u0111\u1ec3 x\u00e1c nh\u1eadn r\u1eb1ng c\u00e1c g\u00f3c con t\u1ea1o th\u00e0nh \u0111\u1ec1u b\u1eb1ng nhau.<\/li>\n<li>Ki\u1ec3m tra t\u1ef7 l\u1ec7 gi\u1eefa c\u00e1c \u0111o\u1ea1n tr\u00ean c\u1ea1nh \u0111\u1ed1i di\u1ec7n \u0111\u1ec3 \u0111\u1ea3m b\u1ea3o ch\u00fang \u0111\u00fang theo t\u1ef7 l\u1ec7 c\u1ee7a c\u00e1c c\u1ea1nh c\u00f2n l\u1ea1i c\u1ee7a tam gi\u00e1c.<\/li>\n<\/ul>\n<p><strong>T\u1ea1i sao vi\u1ec7c hi\u1ec3u v\u1ec1 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c l\u1ea1i quan tr\u1ecdng?<\/strong><\/p>\n<p>Hi\u1ec3u r\u00f5 v\u1ec1 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c v\u00e0 tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec s\u1ebd gi\u00fap b\u1ea1n gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3 v\u00e0 \u00e1p d\u1ee5ng c\u00e1c t\u00ednh ch\u1ea5t h\u00ecnh h\u1ecdc v\u00e0o th\u1ef1c ti\u1ec5n, t\u1eeb thi\u1ebft k\u1ebf ki\u1ebfn tr\u00fac \u0111\u1ebfn ph\u00e2n t\u00edch k\u1ef9 thu\u1eadt.<\/p>\n<p><strong>Nh\u1eefng c\u00f4ng c\u1ee5 n\u00e0o c\u00f3 th\u1ec3 gi\u00fap v\u1ebd \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c ch\u00ednh x\u00e1c?<\/strong><\/p>\n<p>\u0110\u1ec3 v\u1ebd \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c ch\u00ednh x\u00e1c, b\u1ea1n c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng:<\/p>\n<ul>\n<li>Th\u01b0\u1edbc \u0111o g\u00f3c v\u00e0 compa \u0111\u1ec3 \u0111o v\u00e0 chia g\u00f3c.<\/li>\n<li>Ph\u1ea7n m\u1ec1m v\u1ebd h\u00ecnh h\u1ecdc nh\u01b0 GeoGebra ho\u1eb7c AutoCAD \u0111\u1ec3 c\u00f3 s\u1ef1 ch\u00ednh x\u00e1c cao h\u01a1n.<\/li>\n<li>C\u00e1c c\u00f4ng c\u1ee5 v\u1ebd h\u00ecnh h\u1ecdc chuy\u00ean d\u1ee5ng trong c\u00e1c b\u1ed9 d\u1ee5ng c\u1ee5 h\u1ecdc t\u1eadp.<\/li>\n<\/ul>\n<p><strong>\u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u00f3 \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn c\u00e1c thu\u1ed9c t\u00ednh kh\u00e1c c\u1ee7a tam gi\u00e1c kh\u00f4ng?<\/strong><\/p>\n<p>C\u00f3, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u00f3 \u1ea3nh h\u01b0\u1edfng \u0111\u1ebfn c\u00e1c thu\u1ed9c t\u00ednh kh\u00e1c c\u1ee7a tam gi\u00e1c, ch\u1eb3ng h\u1ea1n nh\u01b0:<\/p>\n<ul>\n<li>N\u00f3 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh to\u00e1n c\u00e1c \u0111i\u1ec3m \u0111\u1eb7c bi\u1ec7t nh\u01b0 trung \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp.<\/li>\n<li>\u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u0169ng gi\u00fap trong vi\u1ec7c x\u00e1c \u0111\u1ecbnh c\u00e1c t\u1ef7 l\u1ec7 v\u00e0 t\u00ednh ch\u1ea5t kh\u00e1c c\u1ee7a tam gi\u00e1c trong c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc.<\/li>\n<\/ul>\n<h2>L\u1eddi k\u1ebft<\/h2>\n<p>Trong h\u00ecnh h\u1ecdc, tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? \u0110\u00e2y l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n nh\u01b0ng thi\u1ebft y\u1ebfu c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn g\u00f3c v\u00e0 tam gi\u00e1c. \u0110\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i kh\u00f4ng ch\u1ec9 trong to\u00e1n h\u1ecdc m\u00e0 c\u00f2n trong nhi\u1ec1u l\u0129nh v\u1ef1c nh\u01b0 ki\u1ebfn tr\u00fac, k\u1ef9 thu\u1eadt v\u00e0 thi\u1ebft k\u1ebf, tia ph\u00e2n gi\u00e1c gi\u00fap \u0111\u01a1n gi\u1ea3n h\u00f3a c\u00e1c v\u1ea5n \u0111\u1ec1 ph\u1ee9c t\u1ea1p v\u00e0 t\u1ea1o ra nh\u1eefng c\u1ea5u tr\u00fac \u0111\u1ed1i x\u1ee9ng, ch\u00ednh x\u00e1c.<\/p>\n<p>B\u00e0i vi\u1ebft n\u00e0y \u0111\u00e3 cung c\u1ea5p c\u00e1i nh\u00ecn t\u1ed5ng quan v\u1ec1 tia ph\u00e2n gi\u00e1c, c\u00e1ch nh\u1eadn bi\u1ebft v\u00e0 v\u1ebd n\u00f3, c\u00f9ng v\u1edbi c\u00e1c \u1ee9ng d\u1ee5ng th\u1ef1c ti\u1ec5n v\u00e0 s\u1ef1 kh\u00e1c bi\u1ec7t gi\u1eefa tia ph\u00e2n gi\u00e1c v\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c. Hy v\u1ecdng r\u1eb1ng b\u1ea1n \u0111\u00e3 c\u00f3 c\u00e1i nh\u00ecn r\u00f5 r\u00e0ng v\u1ec1 vai tr\u00f2 c\u1ee7a tia ph\u00e2n gi\u00e1c trong h\u00ecnh h\u1ecdc v\u00e0 c\u00e1ch n\u00f3 gi\u00fap gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3.<\/p>\n<p>\u0110\u1ec3 n\u1eafm v\u1eefng c\u00e1c kh\u00e1i ni\u1ec7m v\u00e0 k\u1ef9 thu\u1eadt li\u00ean quan, \u0111\u1eebng qu\u00ean luy\u1ec7n t\u1eadp v\u1ebd v\u00e0 \u1ee9ng d\u1ee5ng tia ph\u00e2n gi\u00e1c trong c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf. \u0110i\u1ec1u n\u00e0y kh\u00f4ng ch\u1ec9 n\u00e2ng cao kh\u1ea3 n\u0103ng gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n m\u00e0 c\u00f2n m\u1edf r\u1ed9ng kh\u1ea3 n\u0103ng \u1ee9ng d\u1ee5ng trong c\u00e1c l\u0129nh v\u1ef1c c\u1ee7a \u0111\u1eddi s\u1ed1ng.<\/p>\n<p><strong>Xem th\u00eam:<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/so-huu-ti-la-gi\/\">S\u1ed1 h\u1eefu t\u1ec9 l\u00e0 g\u00ec? S\u1ed1 v\u00f4 t\u1ec9 l\u00e0 g\u00ec? \u0110\u1eb7c tr\u01b0ng c\u1ee7a c\u00e1c s\u1ed1 trong To\u00e1n h\u1ecdc<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-to-hop-chinh-hop\/\">B\u1ed9 c\u00f4ng th\u1ee9c Ho\u00e1n v\u1ecb \u2013 Ch\u1ec9nh h\u1ee3p \u2013 T\u1ed5 h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 nh\u1ea5t trong To\u00e1n h\u1ecdc<\/a><\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Trong h\u00ecnh h\u1ecdc, tia ph\u00e2n gi\u00e1c l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng v\u00e0 quen thu\u1ed9c, \u0111\u1eb7c bi\u1ec7t l\u00e0 trong vi\u1ec7c gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n v\u1ec1 tam gi\u00e1c. V\u1eady tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec v\u00e0 l\u00e0m th\u1ebf n\u00e0o \u0111\u1ec3 nh\u1eadn bi\u1ebft c\u0169ng nh\u01b0 \u00e1p d\u1ee5ng trong th\u1ef1c t\u1ebf? B\u00e0i vi\u1ebft n\u00e0y s\u1ebd gi\u1ea3i \u0111\u00e1p nh\u1eefng [&hellip;]<\/p>\n","protected":false},"author":100,"featured_media":374537,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-374436","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>Tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? T\u00ednh ch\u1ea5t ph\u00e2n gi\u00e1c<\/title>\n<meta name=\"description\" content=\"T\u00ecm hi\u1ec3u tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec v\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c l\u00e0 g\u00ec. B\u00e0i vi\u1ebft gi\u00fap b\u1ea1n hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 \u1ee9ng d\u1ee5ng v\u00e0 \u00fd ngh\u0129a c\u1ee7a nh\u1eefng \u0111\u01b0\u1eddng n\u00e0y\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tia-phan-giac-la-gi\/\" \/>\n<meta property=\"og:locale\" content=\"vi_VN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? T\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c\" \/>\n<meta property=\"og:description\" content=\"T\u00ecm hi\u1ec3u tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec v\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c l\u00e0 g\u00ec. B\u00e0i vi\u1ebft gi\u00fap b\u1ea1n hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 \u1ee9ng d\u1ee5ng v\u00e0 \u00fd ngh\u0129a c\u1ee7a nh\u1eefng \u0111\u01b0\u1eddng n\u00e0y\" \/>\n<meta property=\"og:url\" content=\"https:\/\/hoanghamobile.com\/tin-tuc\/tia-phan-giac-la-gi\/\" \/>\n<meta property=\"og:site_name\" content=\"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/hoanghamobilecom\" \/>\n<meta property=\"article:published_time\" content=\"2024-08-13T13:36:19+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2024\/08\/tia-phan-giac-la-gi-avt.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"628\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"L\u00ea Ng\u00e2n\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0110\u01b0\u1ee3c vi\u1ebft b\u1edfi\" \/>\n\t<meta name=\"twitter:data1\" content=\"L\u00ea Ng\u00e2n\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u01af\u1edbc t\u00ednh th\u1eddi gian \u0111\u1ecdc\" \/>\n\t<meta name=\"twitter:data2\" content=\"16 ph\u00fat\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/tia-phan-giac-la-gi\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/tia-phan-giac-la-gi\/\"},\"author\":{\"name\":\"L\u00ea Ng\u00e2n\",\"@id\":\"https:\/\/hoanghamobile.com\/tin-tuc\/#\/schema\/person\/6baed767bcc82aae5b0cab7c7af681a6\"},\"headline\":\"Tia ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? \u0110\u01b0\u1eddng ph\u00e2n gi\u00e1c l\u00e0 g\u00ec? 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