Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00fd Ta l\u00e9t l\u00e0 m\u1ed9t ki\u1ebfn th\u1ee9c r\u1ea5t quan tr\u1ecdng trong To\u00e1n h\u1ecdc, \u0111\u01b0\u1ee3c b\u1ed5 sung v\u00e0o ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc t\u1eeb r\u1ea5t s\u1edbm v\u00e0 c\u00f3 \u1ea3nh h\u01b0\u1edfng r\u1ea5t nhi\u1ec1u \u0111\u1ebfn nh\u1eefng m\u00f4n h\u1ecdc v\u1ec1 sau. Th\u00f4ng qua b\u00e0i vi\u1ebft sau \u0111\u00e2y, Vietlearn s\u1ebd c\u00f9ng c\u00e1c b\u1ea1n \u0111\u1ecdc t\u00ecm hi\u1ec3u th\u1ebf n\u00e0o l\u00e0 \u0111\u1ecbnh l\u00ed Ta l\u00e9t trong tam gi\u00e1c c\u0169ng nh\u01b0 nh\u1eefng h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00fd n\u00e0y.<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00ed Ta l\u00e9t trong tam gi\u00e1c l\u00e0 g\u00ec?<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00ed Ta l\u00e9t hay c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u1ecbnh l\u00fd Thales l\u00e0 m\u1ed9t \u0111\u1ecbnh l\u00fd c\u00f3 vai tr\u00f2 r\u1ea5t quan tr\u1ecdng trong l\u0129nh v\u1ef1c h\u00ecnh h\u1ecdc n\u00f3i ri\u00eang v\u00e0 trong To\u00e1n h\u1ecdc n\u00f3i chung. \u0110\u1ecbnh l\u00fd n\u00e0y \u0111\u01b0\u1ee3c \u0111\u1eb7t theo t\u00ean c\u1ee7a m\u1ed9t nh\u00e0 To\u00e1n h\u1ecdc \u0111\u1ebfn t\u1eeb Hy L\u1ea1p l\u00e0 Thales.<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00ed Ta l\u00e9t trong tam gi\u00e1c<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00ed Ta l\u00e9t trong tam gi\u00e1c \u0111\u01b0\u1ee3c ph\u00e1t bi\u1ec3u r\u1eb1ng khi c\u00f3 1 \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi 1 c\u1ea1nh c\u1ee7a tam gi\u00e1c, \u0111\u1ed3ng th\u1eddi c\u1eaft 2 c\u1ea1nh c\u00f2n l\u1ea1i th\u00ec s\u1ebd \u0111\u1ecbnh ra tr\u00ean 2 c\u1ea1nh \u0111\u01b0\u1ee3c c\u1eaft \u0111\u00f3 nh\u1eefng \u0111o\u1ea1n th\u1eb3ng c\u00f3 t\u1ef7 l\u1ec7 t\u01b0\u01a1ng \u1ee9ng nhau.<\/p>\n\n\n\n
Trong \u25b3ABC, \u0111o\u1ea1n th\u1eb3ng B\u2019C\u2019 \/\/ BC th\u00ec ta s\u1ebd c\u00f3<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00ed Ta l\u00e9t trong tam gi\u00e1c l\u00e0 ki\u1ebfn th\u1ee9c to\u00e1n h\u1ecdc r\u1ea5t quan tr\u1ecdng<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00fd Ta l\u00e9t \u0111\u1ea3o<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00fd Ta l\u00e9t trong tam gi\u00e1c l\u00e0 m\u1ed9t \u0111\u1ecbnh l\u00fd mang t\u00ednh ch\u1ea5t 2 chi\u1ec1u, \u0111\u00f3 l\u00e0 chi\u1ec1u thu\u1eadn v\u00e0 chi\u1ec1u \u0111\u1ea3o ng\u01b0\u1ee3c.<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00fd Ta l\u00e9t \u0111\u1ea3o \u0111\u01b0\u1ee3c ph\u00e1t bi\u1ec3u nh\u01b0 sau: N\u1ebfu trong m\u1ed9t tam gi\u00e1c, m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft 2 c\u1ea1nh c\u1ee7a tam gi\u00e1c \u0111\u00f3 v\u00e0 \u0111\u1ecbnh ra tr\u00ean 2 c\u1ea1nh \u0111\u01b0\u1ee3c c\u1eaft nh\u1eefng \u0111o\u1ea1n th\u1eb3ng t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7 v\u1edbi nhau th\u00ec \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3 s\u1ebd song song v\u1edbi c\u1ea1nh c\u00f2n l\u1ea1i.<\/p>\n\n\n\n
Trong \u25b3ABC, th\u00ec ta s\u1ebd c\u00f3 B\u2019C\u2019 \/\/ BC.<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00fd Ta l\u00e9t thu\u1eadn v\u00e0 \u0111\u1ecbnh l\u00fd Ta l\u00e9t \u0111\u1ea3o c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng \u0111\u01b0\u1ee3c \u0111\u1ed1i v\u1edbi 3 tr\u01b0\u1eddng h\u1ee3p h\u00ecnh v\u1ebd nh\u01b0 sau:<\/p>\n\n\n\n
3 tr\u01b0\u1eddng h\u1ee3p \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Ta l\u00e9t<\/p>\n\n\n\n
Nh\u1eefng h\u1ec7 qu\u1ea3 c\u1ee7a \u0111\u1ecbnh l\u00fd Ta l\u00e9t<\/p>\n\n\n\n
Ti\u1ebfp theo, h\u00e3y c\u00f9ng Vietlearn ph\u00e2n t\u00edch 3 h\u1ec7 qu\u1ea3 quan tr\u1ecdng c\u1ee7a \u0110\u1ecbnh l\u00fd Ta l\u00e9t nh\u00e9.<\/p>\n\n\n\n
H\u1ec7 qu\u1ea3 1<\/p>\n\n\n\n
H\u1ec7 qu\u1ea3 \u0111\u1ea7u ti\u00ean c\u1ee7a \u0111\u1ecbnh l\u00ed Ta l\u00e9t trong tam gi\u00e1c \u0111\u00e3 \u0111\u01b0\u1ee3c ph\u00e1t bi\u1ec3u nh\u01b0 sau: Khi m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi m\u1ed9t c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c c\u00f3 s\u1eb5n, \u0111\u1ed3ng th\u1eddi c\u1eaft 2 c\u1ea1nh c\u00f2n l\u1ea1i th\u00ec s\u1ebd t\u1ea1o ra \u0111\u01b0\u1ee3c m\u1ed9t tam gi\u00e1c m\u1edbi v\u1edbi ba c\u1ea1nh t\u1ec9 l\u1ec7 v\u1edbi ba c\u1ea1nh c\u1ee7a tam gi\u00e1c \u0111\u00e3 \u0111\u01b0\u1ee3c cho tr\u01b0\u1edbc.<\/p>\n\n\n\n
Trong \u25b3ABC, \u0111\u01b0\u1eddng th\u1eb3ng DE \/\/ BC th\u00ec ta s\u1ebd c\u00f3<\/p>\n\n\n\n
\u0110\u1eb7c bi\u1ec7t, h\u1ec7 qu\u1ea3 1 v\u1eabn \u0111\u00fang \u0111\u1ed1i v\u1edbi tr\u01b0\u1eddng h\u1ee3p c\u00f3 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng a song song v\u1edbi 1 c\u1ea1nh c\u1ee7a tam gi\u00e1c \u0111\u00e3 cho v\u00e0 c\u1eaft 2 c\u1ea1nh c\u00f2n l\u1ea1i c\u1ee7a tam gi\u00e1c khi k\u00e9o d\u00e0i.<\/p>\n\n\n\n
H\u1ec7 qu\u1ea3 2<\/p>\n\n\n\n
Ng\u01b0\u1eddi ta ph\u00e1t bi\u1ec3u h\u1ec7 qu\u1ea3 2 c\u1ee7a \u0111\u1ecbnh l\u00fd Ta l\u00e9t nh\u01b0 sau: Khi m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft ngang 2 c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c \u0111\u00e3 cho tr\u01b0\u1edbc v\u00e0 song song v\u1edbi c\u1ea1nh c\u00f2n l\u1ea1i th\u00ec s\u1ebd t\u1ea1o ra \u0111\u01b0\u1ee3c 1 tam gi\u00e1c m\u1edbi v\u00e0 tam gi\u00e1c n\u00e0y \u0111\u1ed3ng d\u1ea1ng v\u1edbi tam gi\u00e1c \u0111\u00e3 \u0111\u01b0\u1ee3c cho tr\u01b0\u1edbc.<\/p>\n\n\n\n
H\u1ec7 qu\u1ea3 3<\/p>\n\n\n\n
H\u1ec7 qu\u1ea3 3 c\u1ee7a \u0111\u1ecbnh l\u00ed Ta l\u00e9t trong tam gi\u00e1c c\u00f2n \u0111\u01b0\u1ee3c bi\u1ebft \u0111\u1ebfn l\u00e0 m\u1ed9t \u0111\u1ecbnh l\u00fd Ta l\u00e9t m\u1edf r\u1ed9ng. Ng\u01b0\u1eddi ta ph\u00e1t bi\u1ec3u \u0111\u1ecbnh l\u00fd m\u1edf r\u1ed9ng nh\u01b0 sau: Khi ba \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy th\u00ec s\u1ebd ch\u1eafn tr\u00ean 2 \u0111\u01b0\u1eddng th\u1eb3ng song song nh\u1eefng c\u1eb7p \u0111o\u1ea1n th\u1eb3ng t\u1ec9 l\u1ec7.<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00fd Ta l\u00e9t trong h\u00ecnh thang<\/p>\n\n\n\n
B\u00ean c\u1ea1nh \u0111\u1ecbnh l\u00ed Ta l\u00e9t trong tam gi\u00e1c, ch\u00fang ta c\u00f2n c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Ta l\u00e9t trong h\u00ecnh thang. Theo \u0111\u00f3, \u0111\u1ecbnh l\u00fd n\u00e0y \u0111\u01b0\u1ee3c ph\u00e1t bi\u1ec3u nh\u01b0 sau: Khi trong m\u1ed9t h\u00ecnh thang, c\u00f3 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng song song c\u00f9ng 2 c\u1ea1nh \u0111\u00e1y, \u0111\u1ed3ng th\u1eddi c\u1eaft 2 c\u1ea1nh b\u00ean c\u1ee7a h\u00ecnh thang \u0111\u00f3 th\u00ec s\u1ebd \u0111\u1ecbnh ra t\u1ea1i 2 c\u1ea1nh b\u00ean \u0111\u00f3 nh\u1eefng \u0111o\u1ea1n th\u1eb3ng c\u00f3 t\u1ef7 l\u1ec7 t\u01b0\u01a1ng \u1ee9ng v\u1edbi nhau.<\/p>\n\n\n\n
V\u00ed d\u1ee5, khi cho m\u1ed9t h\u00ecnh thang ABCD, \u0111i\u1ec3m E thu\u1ed9c \u0111o\u1ea1n AD, \u0111i\u1ec3m F thu\u1ed9c \u0111o\u1ea1n BC. N\u1ebfu \u0111o\u1ea1n EF \/\/ AB \/\/ CD th\u00ec ta s\u1ebd c\u00f3 v\u00e0 ng\u01b0\u1ee3c l\u1ea1i, trong h\u00ecnh thang ABCD, n\u1ebfu ta c\u00f3 th\u00ec EF \/\/ AB \/\/ CD.<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00fd Ta l\u00e9t trong kh\u00f4ng gian<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00fd Ta l\u00e9t c\u0169ng \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng \u0111\u1ed1i v\u1edbi h\u00ecnh h\u1ecdc kh\u00f4ng gian. Theo \u0111\u00f3, \u0111\u1ecbnh l\u00fd Ta l\u00e9t trong kh\u00f4ng gian \u0111\u01b0\u1ee3c ph\u00e1t bi\u1ec3u nh\u01b0 sau: 3 m\u1eb7t ph\u1eb3ng song song trong kh\u00f4ng gian s\u1ebd ch\u1eafn tr\u00ean 2 \u0111\u01b0\u1eddng th\u1eb3ng nh\u1eefng \u0111o\u1ea1n th\u1eb3ng c\u00f3 t\u1ef7 l\u1ec7 t\u01b0\u01a1ng \u1ee9ng nhau.<\/p>\n\n\n\n
Ngo\u00e0i ra, ng\u01b0\u1eddi ta c\u00f2n ph\u00e1t tri\u1ec3n \u0111\u1ecbnh l\u00fd \u0111\u1ea3o c\u1ee7a \u0111\u1ecbnh l\u00fd Ta l\u00e9t trong kh\u00f4ng gian v\u00e0 \u0111\u1ecbnh l\u00fd \u0111\u1ea3o \u0111\u01b0\u1ee3c ph\u00e1t bi\u1ec3u nh\u01b0 sau: V\u1edbi 2 \u0111\u01b0\u1eddng th\u1eb3ng d1 v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng d2 ch\u00e9o nhau, nh\u1eefng \u0111i\u1ec3m A1, B1, C1 \u2208 (d1) v\u00e0 A2, B2, C2 \u2208 (d2) v\u00e0 th\u00ec nh\u1eefng \u0111\u01b0\u1eddng th\u1eb3ng A1A2, B1B2, C1C2 s\u1ebd c\u00f9ng song song v\u1edbi m\u1ed9t m\u1eb7t ph\u1eb3ng.<\/p>\n\n\n\n
Nh\u1eefng \u1ee9ng d\u1ee5ng c\u1ee7a \u0111\u1ecbnh l\u00fd Ta l\u00e9t<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00fd Ta l\u00e9t \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng r\u1ea5t r\u1ed9ng r\u00e3i, \u0111\u1eb7c bi\u1ec7t l\u00e0 khi \u0111o \u0111\u1ea1c nh\u1eefng k\u00edch th\u01b0\u1edbc qu\u00e1 l\u1edbn v\u00e0 kh\u00f4ng th\u1ec3 tr\u1ef1c ti\u1ebfp \u0111o \u0111\u01b0\u1ee3c. \u0110\u1ecbnh l\u00fd Ta l\u00e9t \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng trong 2 v\u00ed d\u1ee5 \u0111i\u1ec3n h\u00ecnh nh\u01b0 sau:<\/p>\n\n\n\n
\u0110o \u0111\u1ea1c kho\u1ea3ng c\u00e1ch \u1edf gi\u1eefa 2 b\u1edd s\u00f4ng v\u00e0 kh\u00f4ng c\u1ea7n ph\u1ea3i sang s\u00f4ng.<\/p>\n\n\n\n
\u0110o chi\u1ec1u cao c\u1ee7a c\u00e1c v\u1eadt d\u1ee5ng b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng b\u00f3ng m\u1eb7t tr\u1eddi.<\/p>\n\n\n\n
\u0110\u1ecbnh l\u00fd Ta l\u00e9t \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng r\u1ea5t r\u1ed9ng r\u00e3i trong th\u1ef1c ti\u1ec5n<\/p>\n\n\n\n
Nh\u01b0 v\u1eady, qua b\u00e0i vi\u1ebft tr\u00ean c\u1ee7a Vietlearn, c\u00f3 th\u1ec3 th\u1ea5y r\u1eb1ng \u0111\u1ecbnh l\u00ed Ta l\u00e9t trong tam gi\u00e1c l\u00e0 m\u1ed9t ph\u1ea7n r\u1ea5t quan tr\u1ecdng trong To\u00e1n h\u1ecdc v\u00e0 \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng r\u1ea5t r\u1ed9ng r\u00e3i trong th\u1ef1c t\u1ebf. \u0110\u1ec3 t\u00ecm hi\u1ec3u th\u00eam nhi\u1ec1u ki\u1ebfn th\u1ee9c kh\u00e1c, h\u00e3y truy c\u1eadp ngay v\u00e0o trang web Vietlearn.org\/ nh\u00e9.<\/p>\n\n\n\n
<\/p>\n\n\n\n
Kh\u00e1i ni\u1ec7m tam gi\u00e1c \u0111\u1ed3ng d\u1ea1ng<\/p>\n\n\n\n
C\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1ed3ng d\u1ea1ng c\u1ee7a tam gi\u00e1c vu\u00f4ng \u2013 H\u1ecdc<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn \u0110\u1ecbnh l\u00fd Ta l\u00e9t l\u00e0 m\u1ed9t ki\u1ebfn th\u1ee9c r\u1ea5t quan tr\u1ecdng trong To\u00e1n h\u1ecdc, \u0111\u01b0\u1ee3c b\u1ed5 sung v\u00e0o ch\u01b0\u01a1ng tr\u00ecnh h\u1ecdc t\u1eeb r\u1ea5t s\u1edbm v\u00e0 c\u00f3 \u1ea3nh h\u01b0\u1edfng r\u1ea5t nhi\u1ec1u \u0111\u1ebfn nh\u1eefng m\u00f4n h\u1ecdc v\u1ec1 sau. Th\u00f4ng qua b\u00e0i vi\u1ebft sau \u0111\u00e2y, Vietlearn s\u1ebd c\u00f9ng c\u00e1c b\u1ea1n \u0111\u1ecdc t\u00ecm […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[9],"tags":[],"class_list":["post-915","post","type-post","status-publish","format-standard","hentry","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/915","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=915"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/915\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=915"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=915"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=915"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}