Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
Ng\u00e0y nay, vi\u1ec7c h\u1ecdc to\u00e1n ng\u00e0y kh\u00f3 s\u1ed1 l\u01b0\u1ee3ng ki\u1ebfn th\u1ee9c c\u1ea7n ph\u1ea3i ti\u1ebfp thu r\u1ea5t l\u00e0 nhi\u1ec1u, v\u00ec v\u1eady r\u1ea5t nhi\u1ec1u h\u1ecdc sinh<\/a> c\u1ea3m th\u1ea5y ch\u00e1n n\u1ea3n v\u00ec kh\u00f4ng th\u1ec3 nh\u1edb h\u1ebft \u0111\u01b0\u1ee3c. Hi\u1ec3u \u0111\u01b0\u1ee3c s\u1ef1 kh\u00f3 kh\u0103n trong vi\u1ec7c ghi nh\u1edb m\u00f4n to\u00e1n, h\u00f4m nay Vietlearn s\u1ebd g\u1eedi \u0111\u1ebfn cho c\u00e1c b\u1ea1n m\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c v\u00e0 d\u1ea1ng b\u00e0i th\u01b0\u1eddng g\u1eb7p \u0111\u1ec3 cho b\u1ea1n c\u00f3 th\u1ec3 d\u1ec5 d\u00e0ng h\u1ecdc h\u01a1n.<\/p>\n\n\n\n T\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t \u0111o\u1ea1n th\u1eb3ng<\/p>\n\n\n\n \u0110\u1ecbnh ngh\u0129a: \u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t \u0111o\u1ea1n th\u1eb3ng l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0111i trung \u0111i\u1ec3m v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi \u0111o\u1ea1n th\u1eb3ng \u1ea5y.<\/p>\n\n\n\n T\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng<\/p>\n\n\n\n D l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng AB<\/p>\n\n\n\n \u0110\u1ecbnh l\u00fd 1: \u0110i\u1ec3m n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c th\u00ec c\u00e1ch \u0111\u1ec1u hai m\u00fat c\u1ee7a \u0111o\u1ea1n th\u1eb3ng \u0111\u00f3.<\/p>\n\n\n\n V\u00ed d\u1ee5: d l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng AB, M l\u00e0 m\u1ed9t \u0111i\u1ec3m n\u1eb1m tr\u00ean d => MA = MB<\/p>\n\n\n\n \u0110\u1ecbnh l\u00fd 2: \u0110i\u1ec3m c\u00e1ch \u0111\u1ec1u hai m\u00fat c\u1ee7a \u0111o\u1ea1n th\u1eb3ng th\u00ec n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng \u0111\u00f3.<\/p>\n\n\n\n V\u00ed d\u1ee5: MA = MB th\u00ec ta c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh r\u1eb1ng M n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng AB<\/p>\n\n\n\n T\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t tam gi\u00e1c<\/p>\n\n\n\n \u0110\u1ecbnh l\u00fd 3: Trong m\u1ed9t tam gi\u00e1c c\u00e2n \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t c\u1ea1nh \u0111\u1ed3ng th\u1eddi c\u0169ng s\u1ebd l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn \u0111\u1ed1i v\u1edbi c\u1ea1nh \u0111\u00f3.<\/p>\n\n\n\n V\u00ed d\u1ee5: AM l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ee7a c\u1ea1nh BC \u0111\u1ed3ng th\u1eddi AM c\u0169ng l\u00e0 c\u0169ng l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a c\u1ea1nh BC.<\/p>\n\n\n\n \u0110\u01b0\u1eddng trung tr\u1ef1c trong tam gi\u00e1c c\u00e2n<\/p>\n\n\n\n \u0110\u1ecbnh l\u00fd 4: N\u1ebfu ba \u0111\u01b0\u1eddng th\u1eb3ng trung tr\u1ef1c c\u1ee7a m\u1ed9t tam gi\u00e1c c\u00f9ng \u0111i qua m\u1ed9t \u0111i\u1ec3m th\u00ec \u0111i\u1ec3m n\u00e0y s\u1ebd c\u00e1ch \u0111\u1ec1u 3 \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c \u0111\u00f3.<\/p>\n\n\n\n V\u00ed d\u1ee5: Cho tam gi\u00e1c ABC, 3 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c \u0111\u1ec1u giao t\u1ea1i m\u1ed9t \u0111i\u1ec3m O<\/p>\n\n\n\n => OA = OB = OC => \u0110i\u1ec3m O ch\u00ednh l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp c\u1ee7a tam gi\u00e1c ABC<\/p>\n\n\n\n O l\u00e0 t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp c\u1ee7a tam gi\u00e1c ABC<\/p>\n\n\n\n T\u00ednh ch\u1ea5t ba \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c \u2013 H\u1ecdc to\u00e1n c\u00f9ng Vietlearn<\/p><\/blockquote>\n\n\n\n C\u00e1c d\u1ea1ng b\u00e0i to\u00e1n th\u01b0\u1eddng g\u1eb7p<\/p>\n\n\n\n D\u1ea1ng 1: Ch\u1ee9ng minh \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t \u0111o\u1ea1n th\u1eb3ng<\/p>\n\n\n\n \u0110\u1ec3 c\u00f3 th\u1ec3 ch\u1ee9ng minh d l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng AB, ta ch\u1ec9 c\u1ea7n ch\u1ee9ng minh hai \u0111i\u1ec3m A v\u00e0 ch\u1ee9a c\u00e1c \u0111i\u1ec3m c\u00e1ch \u0111\u1ec1u d ho\u1eb7c s\u1eed d\u1ee5ng \u0111\u1ecbnh ngh\u0129a v\u1ec1 t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh.<\/p>\n\n\n\n D\u1ea1ng 2: Ch\u1ee9ng minh hai \u0111o\u1ea1n th\u1eb3ng b\u1eb1ng nhau<\/p>\n\n\n\n S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00fd s\u1ed5 1 \u0111\u1ec3 t\u00ecm ra c\u00e1ch ch\u1ee9ng minh nhanh nh\u1ea5t.<\/p>\n\n\n\n \u0110\u1ecbnh l\u00fd 3: \u0110i\u1ec3m n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c th\u00ec c\u00e1ch \u0111\u1ec1u hai m\u00fat c\u1ee7a \u0111o\u1ea1n th\u1eb3ng \u0111\u00f3.<\/p>\n\n\n\n D\u1ea1ng 3: B\u00e0i t\u1eadp v\u1ec1 t\u00ednh gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t<\/p>\n\n\n\n \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c \u0111\u1ec3 c\u00f3 th\u1ec3 thay \u0111\u1ed5i \u0111\u1ed9 d\u00e0i c\u1ee7a m\u1ed9t \u0111o\u1ea1n th\u1eb3ng th\u00e0nh m\u1ed9t con s\u1ed1 chi\u1ec1u d\u00e0i c\u1ee7a m\u1ed9t \u0111o\u1ea1n th\u1eb3ng kh\u00e1c b\u1eb1ng n\u00f3. Sau \u0111\u00f3 s\u1eed d\u1ee5ng bn b\u1ea5t \u0111\u1eb3ng th\u1ee9c c\u1ee7a tam gi\u00e1c \u0111\u1ec3 t\u00ecm \u0111\u01b0\u1ee3c gi\u00e1 tr\u1ecb nh\u1ecf nh\u1ea5t.<\/p>\n\n\n\n D\u1ea1ng 4: X\u00e1c \u0111\u1ecbnh t\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c<\/p>\n\n\n\n S\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00fd s\u1ed5 4 \u0111\u1ec3 t\u00ecm ra c\u00e1ch ch\u1ee9ng minh nhanh nh\u1ea5t.<\/p>\n\n\n\n \u0110\u1ecbnh l\u00fd 4: N\u1ebfu ba \u0111\u01b0\u1eddng th\u1eb3ng trung tr\u1ef1c c\u1ee7a m\u1ed9t tam gi\u00e1c c\u00f9ng \u0111i qua m\u1ed9t \u0111i\u1ec3m th\u00ec \u0111i\u1ec3m n\u00e0y s\u1ebd c\u00e1ch \u0111\u1ec1u 3 \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c \u0111\u00f3.<\/p>\n\n\n\n D\u1ea1ng 5: B\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t tam gi\u00e1c c\u00e2n<\/p>\n\n\n\n \u0110\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c d\u1ea1ng b\u00e0i t\u1eadp n\u00e0y, b\u1ea1n n\u00ean ch\u00fa \u00fd r\u1eb1ng trong m\u1ed9t c\u00e2n \u0111\u01b0\u1eddng trung tr\u1ef1c c\u0169ng ch\u00ednh l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c \u1ee9ng v\u1edbi c\u1ea1nh \u0111\u00e1y.<\/p>\n\n\n\n D\u1ea1ng 6: B\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t tam gi\u00e1c vu\u00f4ng<\/p>\n\n\n\n B\u1ea1n ch\u1ec9 c\u1ea7n nh\u1edb, trong m\u1ed9t tam gi\u00e1c vu\u00f4ng giao \u0111i\u1ec3m \u0111\u01b0\u1eddng trung tr\u1ef1c l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh huy\u1ec1n.<\/p>\n\n\n\n B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng<\/p>\n\n\n\n B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng v\u1ec1 \u0111\u01b0\u1eddng trung tr\u1ef1c<\/p>\n\n\n\n C\u00e2u 1: G\u1ecdi O l\u00e0 \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c ABC. Khi \u0111\u00f3 O l\u00e0:<\/p>\n\n\n\n \u0110i\u1ec3m c\u00e1ch \u0111\u1ec1u 3 c\u1ea1nh c\u1ee7a tam gi\u00e1c ABC<\/p>\n\n\n\n \u0110i\u1ec3m c\u00e1ch \u0111\u1ec1u 3 \u0111\u1ec9nh c\u1ee7a tam gi\u00e1c ABC<\/p>\n\n\n\n T\u00e2m \u0111\u01b0\u1eddng \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp tam gi\u00e1c ABC<\/p>\n\n\n\n \u0110\u00e1p \u00e1n B v\u00e0 C \u0111\u00fang<\/p>\n\n\n\n C\u00e2u 2: N\u1ebfu m\u1ed9t tam gi\u00e1c c\u00f3 m\u1ed9t \u0111\u01b0\u1eddng trung tuy\u1ebfn \u0111\u1ed3ng th\u1eddi l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c th\u00ec tam gi\u00e1c \u0111\u00f3 l\u00e0 tam gi\u00e1c g\u00ec?<\/p>\n\n\n\n Tam gi\u00e1c vu\u00f4ng<\/p>\n\n\n\n Tam gi\u00e1c c\u00e2n<\/p>\n\n\n\n Tam gi\u00e1c \u0111\u1ec1u<\/p>\n\n\n\n Tam gi\u00e1c vu\u00f4ng c\u00e2n<\/p>\n\n\n\n C\u00e2u 3: Tr\u00ean \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng AB l\u1ea5y \u0111i\u1ec3m M. H\u1ea1 MH\u22a5AB. Tr\u00ean \u0111o\u1ea1n MH l\u1ea5y \u0111i\u1ec3m P, g\u1ecdi E l\u00e0 giao \u0111i\u1ec3m c\u1ee7a MB v\u1edbi AP. G\u1ecdi F l\u00e0 giao \u0111i\u1ec3m c\u1ee7a BP v\u1edbi MA<\/p>\n\n\n\n Ch\u1ee9ng minh MH l\u00e0 ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c AMB<\/p>\n\n\n\n Ch\u1ee9ng minh MH l\u00e0 trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng EF<\/p>\n\n\n\n Ch\u1ee9ng minh AF= BE<\/p>\n\n\n\n C\u00e2u 4: Cho tam gi\u00e1c \u25b3ABC c\u00e2n t\u1ea1i A. Hai \u0111\u01b0\u1eddng trung tuy\u1ebfn CN v\u00e0 BM c\u1eaft nhau t\u1ea1i I. Hai tia ph\u00e2n gi\u00e1c trong c\u1ee7a B v\u00e0 C c\u1eaft nhau t\u1ea1i O. Hai \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a 2 c\u1ea1nh AB, AC c\u1eaft nhau t\u1ea1i K.<\/p>\n\n\n\n Ch\u1ee9ng minh r\u1eb1ng: BM = CN.<\/p>\n\n\n\n Ch\u1ee9ng minh r\u1eb1ng OB = OC<\/p>\n\n\n\n Ch\u1ee9ng minh 4 \u0111i\u1ec3m A,O, I, K th\u1eb3ng h\u00e0ng.<\/p>\n\n\n\n C\u00e2u 5: Cho g\u00f3c xOy = 50\u00ba, \u0111i\u1ec3m A n\u1eb1m trong g\u00f3c xOy. V\u1ebd \u0111i\u1ec3m M sao cho Ox l\u00e0 trung tr\u1ef1c c\u1ee7a AN, v\u1ebd \u0111i\u1ec3m M sao cho Oy l\u00e0 trung tr\u1ef1c c\u1ee7a AM.<\/p>\n\n\n\n Ch\u1ee9ng minh r\u1eb1ng OM = ON<\/p>\n\n\n\n T\u00ednh s\u1ed1 \u0111o MON<\/p>\n\n\n\n L\u1eddi k\u1ebft<\/p>\n\n\n\n Tr\u00ean \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n<\/a> v\u1ec1 t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng, m\u1ed9t tam gi\u00e1c m\u00e0 Vietlearn mu\u1ed1n g\u1eedi \u0111\u1ebfn cho c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a>. Hy v\u1ecdng b\u00e0i vi\u1ebft b\u1ed5 \u00edch n\u00e0y s\u1ebd gi\u00fap c\u00e1c b\u1ea1n d\u1ec5 d\u00e0ng ti\u1ebfp thu ki\u1ebfn th\u1ee9c v\u1ec1 t\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung tr\u1ef1c h\u01a1n. N\u1ebfu c\u00e1c b\u1ea1n c\u00f2n mu\u1ed1n t\u00ecm hi\u1ec3u th\u00eam c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n kh\u00e1c th\u00ec hay truy c\u1eadp ngay v\u00e0o website: Vietlearn.org\/ c\u1ee7a ch\u00fang t\u00f4i \u0111\u1ec3 t\u00ecm hi\u1ec3u nh\u00e9!<\/p>\n\n\n\n Xem ngay:<\/p>\n\n\n\n T\u00ednh ch\u1ea5t ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a tam gi\u00e1c<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":" Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn Ng\u00e0y nay, vi\u1ec7c h\u1ecdc to\u00e1n ng\u00e0y kh\u00f3 s\u1ed1 l\u01b0\u1ee3ng ki\u1ebfn th\u1ee9c c\u1ea7n ph\u1ea3i ti\u1ebfp thu r\u1ea5t l\u00e0 nhi\u1ec1u, v\u00ec v\u1eady r\u1ea5t nhi\u1ec1u h\u1ecdc sinh c\u1ea3m th\u1ea5y ch\u00e1n n\u1ea3n v\u00ec kh\u00f4ng th\u1ec3 nh\u1edb h\u1ebft \u0111\u01b0\u1ee3c. Hi\u1ec3u \u0111\u01b0\u1ee3c s\u1ef1 kh\u00f3 kh\u0103n trong vi\u1ec7c ghi nh\u1edb m\u00f4n to\u00e1n, h\u00f4m nay Vietlearn s\u1ebd […]<\/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":[1],"tags":[],"class_list":["post-977","post","type-post","status-publish","format-standard","hentry","category-general"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/977","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=977"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/977\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=977"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=977"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}