Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
B\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y, Vietlearn s\u1ebd t\u1ed5ng h\u1ee3p c\u00e1c ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n<\/a> v\u1ec1 t\u00ednh ch\u1ea5t c\u1ee7a hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau m\u1ed9t c\u00e1ch d\u1ec5 hi\u1ec3u v\u00e0 kh\u00e1i qu\u00e1t nh\u1ea5t cho c\u00e1c b\u1ea1n. Bao g\u1ed3m c\u00e1c c\u00f4ng th\u1ee9c, \u0111\u1ecbnh l\u00fd c\u1ea7n thi\u1ebft v\u00e0 \u0111\u1eb7c bi\u1ec7t l\u00e0 m\u1ed9t s\u1ed1 d\u1ea1ng to\u00e1n th\u01b0\u1eddng g\u1eb7p v\u1ec1 c\u00e1c t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau.<\/p>\n\n\n\n M\u1eafc d\u00f9 c\u00e1c b\u00e0i gi\u1ea3ng t\u00ednh ch\u1ea5t c\u1ee7a hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau xu\u1ea5t hi\u1ec7n \u1edf l\u1edbp 9 nh\u1eefng d\u1ea1ng b\u00e0i n\u00e0y s\u1ebd xuy\u00ean su\u1ed1t qu\u00e1 tr\u00ecnh h\u1ecdc trung h\u1ecdc. \u0110\u00e2y c\u0169ng l\u00e0 m\u1ed9t m\u1ea3ng ki\u1ebfn th\u1ee9c kh\u00f4ng th\u1ec3 thi\u1ebfu trong thi \u0111\u1ea1i h\u1ecdc. V\u1eady n\u00ean h\u00e3y h\u1ecdc t\u1eadp<\/a> ch\u0103m ch\u1ec9 v\u00e0 ch\u00fa \u00fd v\u1edbi nh\u1eefng g\u00ec Vietlearn \u0111\u1ec1 c\u1eadp trong b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y nh\u00e9!<\/p>\n\n\n\n Ti\u1ebfp tuy\u1ebfn \u2013 ti\u1ebfp \u0111i\u1ec3m<\/p>\n\n\n\n \u0110\u1ec3 c\u00f3 th\u1ec3 hi\u1ec3u r\u00f5 \u0111\u01b0\u1ee3c v\u1ea5n \u0111\u1ec1 th\u00ec \u0111i\u1ec1u \u0111\u1ea7u ti\u00ean \u0111\u00f3 l\u00e0 c\u00f3 th\u1ec3 hi\u1ec3u \u0111\u01b0\u1ee3c kh\u00e1i ni\u1ec7m c\u1ee7a nh\u1eefng y\u1ebfu t\u1ed1 ch\u00ednh trong kh\u00e1i ni\u1ec7m \u0111\u00f3. Vietlearn s\u1ebd mang t\u1edbi cho b\u1ea1n \u0111\u1ecbnh ngh\u0129a chi ti\u1ebft v\u00e0 gi\u00fap b\u1ea1n hi\u1ec3u \u0111\u01b0\u1ee3c ti\u1ebfp tuy\u1ebfn ngh\u0129a l\u00e0 g\u00ec.<\/p>\n\n\n\n Ti\u1ebfp tuy\u1ebfn l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ec9 \u201cch\u1ea1m\u201d \u0111\u01b0\u1eddng cong t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t thu\u1ed9c \u0111\u01b0\u1eddng cong. \u0110i\u1ec3m c\u1eaft duy nh\u1ea5t gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 \u0111\u01b0\u1eddng cong \u0111\u00f3 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ti\u1ebfp \u0111i\u1ec3m. Hai kh\u00e1i ni\u1ec7m n\u00e0y l\u00e0 nh\u1eefng kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n nh\u1ea5t c\u1ee7a ph\u1ea7n to\u00e1n h\u00ecnh h\u1ecdc vi ph\u00e2n v\u00e0 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng r\u1ed9ng r\u00e3i t\u1eeb nh\u1eefng b\u00e0i to\u00e1n c\u01a1 b\u1ea3n cho t\u1edbi nh\u1eefng b\u00e0i to\u00e1n n\u00e2ng cao ph\u1ee9c t\u1ea1p.<\/p>\n\n\n\n T\u00ednh ch\u1ea5t c\u1ee7a hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau<\/p>\n\n\n\n Ti\u1ebfp tuy\u1ebfn \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 giao t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t. N\u1ebfu hai ti\u1ebfp tuy\u1ebfn tr\u00ean c\u00f9ng m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n c\u1eaft nhau th\u00ec s\u1ebd c\u00f3 nh\u1eefng t\u00ednh ch\u1ea5t nh\u01b0 sau:<\/p>\n\n\n\n \u0110i\u1ec3m c\u1eaft nhau c\u1ee7a hai ti\u1ebfp tuy\u1ebfn ngo\u00e0i \u0111\u01b0\u1eddng tr\u00f2n th\u00ec c\u00e1ch \u0111\u1ec1u hai ti\u1ebfp \u0111i\u1ec3m<\/p>\n\n\n\n Tia ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c h\u1ee3p b\u1edfi hai ti\u1ebfp tuy\u1ebfn th\u00ec \u0111i qua t\u00e2m<\/p>\n\n\n\n Tia n\u1ed1i t\u1eeb t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n t\u1edbi \u0111i\u1ec3m giao nhau c\u1ee7a hai ti\u1ebfp tuy\u1ebfn l\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a g\u00f3c t\u1ea1o b\u1edfi hai b\u00e1n k\u00ednh vu\u00f4ng g\u00f3c v\u1edbi ti\u1ebfp tuy\u1ebfn \u0111\u00f3<\/p>\n\n\n\n T\u00ednh ch\u1ea5t c\u1ee7a hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau<\/p>\n\n\n\n \u0110\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp, ngo\u1ea1i ti\u1ebfp c\u1ee7a m\u1ed9t tam gi\u00e1c<\/p>\n\n\n\n \u0110\u01b0\u1eddng tr\u00f2n ti\u1ebfp x\u00fac t\u1ea1i m\u1ed9t \u0111i\u1ec3m v\u1edbi m\u1ed7i c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c hay \u0111a gi\u00e1c th\u00ec \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp hay \u0111a gi\u00e1c \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111a gi\u00e1c ngo\u1ea1i ti\u1ebfp<\/p>\n\n\n\n \u0110\u01b0\u1eddng tr\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ngo\u1ea1i ti\u1ebfp khi \u0111\u01b0\u1eddng tr\u00f2n \u0111\u00f3 \u0111i qua t\u1ea5t c\u1ea3 c\u00e1c \u0111\u1ec9nh c\u1ee7a m\u1ed9t \u0111a gi\u00e1c.<\/p>\n\n\n\n C\u00e1c \u0111a gi\u00e1c ch\u1ec9 c\u00f3 duy nh\u1ea5t m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp v\u00e0 ngo\u00e0i ti\u1ebfp cho m\u1ed7i \u0111a gi\u00e1c kh\u00e1c nhau<\/p>\n\n\n\n Trong m\u00f4n h\u1ecdc to\u00e1n 9 t\u00ednh ch\u1ea5t hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau, ta c\u00f3 th\u1ec3 r\u00fat ra th\u00eam m\u1ed9t \u0111\u1eb7c \u0111i\u1ec3m. \u0110\u00f3 l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp c\u1ee7a m\u1ed9t tam gi\u00e1c s\u1ebd l\u00e0 giao \u0111i\u1ec3m c\u1ee7a c\u00e1c \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c c\u1ee7a c\u00e1c g\u00f3c thu\u1ed9c tam gi\u00e1c ngo\u1ea1i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n.<\/p>\n\n\n\n C\u00f3 m\u1ed9t s\u1ed1 \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp v\u00e0 ngo\u1ea1i ti\u1ebfp tam gi\u00e1c c\u1ea7n ch\u00fa \u00fd \u0111\u1ec3 c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng v\u00e0o b\u00e0i t\u1eadp nh\u01b0 sau:<\/p>\n\n\n\n T\u00e2m \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp c\u1ee7a m\u1ed9t tam gi\u00e1c l\u00e0 giao \u0111i\u1ec3m c\u1ee7a ba \u0111\u01b0\u1eddng trung tr\u1ef1c k\u1ebb t\u1eeb ba c\u1ea1nh c\u1ee7a tam gi\u00e1c \u0111\u00f3.<\/p>\n\n\n\n Trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh huy\u1ec1n ch\u00ednh l\u00e0 t\u00e2m c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp n\u1ebfu tam gi\u00e1c \u0111\u00f3 l\u00e0 tam gi\u00e1c vu\u00f4ng.<\/p>\n\n\n\n Kh\u00e1c v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp, \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp c\u00f3 t\u00e2m l\u00e0 giao c\u1ee7a ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c t\u1eeb \u0111\u1ec9nh c\u1ee7a ba g\u00f3c thu\u1ed9c tam gi\u00e1c.<\/p>\n\n\n\n \u0110\u01b0\u1eddng tr\u00f2n b\u00e0ng ti\u1ebfp c\u1ee7a m\u1ed9t tam gi\u00e1c<\/p>\n\n\n\n \u0110\u01b0\u1eddng tr\u00f2n c\u00f3 hai ph\u1ea7n ti\u1ebfp x\u00fac v\u1edbi m\u1ed9t c\u1ea1nh c\u1ee7a tam gi\u00e1c v\u00e0 ph\u1ea7n c\u00f2n l\u1ea1i ti\u1ebfp x\u00fac v\u1edbi ph\u1ea7n k\u00e9o d\u00e0i c\u1ee7a hai c\u1ea1nh kh\u00e1c c\u1ee7a tam gi\u00e1c g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n b\u00e0ng ti\u1ebfp c\u1ee7a m\u1ed9t tam gi\u00e1c.<\/p>\n\n\n\n \u0110\u01b0\u1eddng tr\u00f2n b\u00e0ng ti\u1ebfp<\/p>\n\n\n\n T\u00e2m c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n b\u00e0ng ti\u1ebfp s\u1ebd n\u1eb1m \u1edf trong g\u00f3c A v\u00e0 thu\u1ed9c \u0111i\u1ec3m c\u1eaft c\u1ee7a ph\u00e2n gi\u00e1c ngo\u00e0i c\u1ee7a g\u00f3c B v\u00e0 g\u00f3c C. Ho\u1eb7c c\u0169ng c\u00f3 th\u1ec3 l\u00e0 \u0111i\u1ec3m \u0111\u1ed3ng quy c\u1ee7a ba \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c g\u00f3c A, \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c g\u00f3c ngo\u00e0i c\u1ee7a B v\u00e0 C. M\u1ed7i tam gi\u00e1c th\u01b0\u1eddng c\u00f3 ba \u0111\u01b0\u1eddng tr\u00f2n b\u00e0ng ti\u1ebfp kh\u00e1c nhau.<\/p>\n\n\n\n C\u00e1c d\u1ea1ng b\u00e0i t\u1eadp v\u1ec1 t\u00ednh ch\u1ea5t c\u1ee7a hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau.<\/p>\n\n\n\n \u1ede l\u1edbp 9, c\u00e1c b\u1ea1n s\u1ebd \u0111\u01b0\u1ee3c l\u00e0m quen v\u1edbi nhi\u1ec1u b\u00e0i to\u00e1n l\u00e0 k\u1ebft h\u1ee3p c\u1ee7a nhi\u1ec1u d\u1ea1ng to\u00e1n v\u00e0 \u0111\u1ecbnh l\u00fd kh\u00e1c nhau. Nh\u1eefng d\u1ea1ng b\u00e0i to\u00e1n c\u00f3 li\u00ean quan t\u1edbi t\u00ednh ch\u1ea5t c\u1ee7a hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau \u0111\u01b0\u1ee3c chia l\u00e0m hai lo\u1ea1i c\u01a1 b\u1ea3n:<\/p>\n\n\n\n Ch\u1ee9ng minh c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 song song, vu\u00f4ng g\u00f3c, b\u1eb1ng nhau, ho\u1eb7c t\u1ec9 l\u1ec7 v\u1edbi nhau d\u1ef1a v\u00e0o c\u00e1c t\u00ednh ch\u1ea5t \u0111\u00e3 n\u00eau tr\u00ean.<\/p>\n\n\n\n Ch\u1ee9ng minh m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua \u0111\u01b0\u1eddng tr\u00f2n l\u00e0 ti\u1ebfp tuy\u1ebfn. Sau khi ch\u1ee9ng minh th\u00ec t\u00ednh c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng ch\u00ednh x\u00e1c cho c\u00e1c c\u1ea1nh, c\u00e1c g\u00f3c v\u00e0 c\u00e1c t\u1ec9 l\u1ec7 \u0111\u1ec1 b\u00e0i y\u00eau c\u1ea7u kh\u00e1c. V\u1edbi b\u00e0i to\u00e1n n\u00e0y, h\u1ecdc sinh<\/a> c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng c\u00e1c \u0111\u1ecbnh l\u00fd, h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng hay c\u00e1c t\u00ednh ch\u1ea5t li\u00ean quan t\u1edbi tam gi\u00e1c v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n ngo\u00e0i c\u00e1c t\u00ednh ch\u1ea5t c\u1ee7a hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau.<\/p>\n\n\n\n B\u00e0i t\u1eadp minh h\u1ecda<\/p>\n\n\n\n C\u00e1c b\u00e0i to\u00e1n v\u1ec1 ti\u1ebfp tuy\u1ebfn lu\u00f4n l\u00e0 nh\u1eefng b\u00e0i to\u00e1n l\u00e0m c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a> \u0111au \u0111\u1ea7u. Kh\u00f4ng ch\u1ec9 l\u00e0 nh\u1eefng b\u00e0i ch\u1ee9ng minh \u0111\u01a1n gi\u1ea3n c\u01a1 b\u1ea3n l\u1edbp 9, c\u00e1c \u0111\u01b0\u1eddng ti\u1ebfp tuy\u1ebfn c\u00f2n theo c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a> xuy\u00ean su\u1ed1t t\u1edbi c\u00e1c b\u00e0i to\u00e1n \u00f4n thi \u0111\u1ea1i h\u1ecdc<\/a>. Ch\u00ednh v\u00ec v\u1eady, qua b\u00e0i vi\u1ebft tr\u00ean Vietlearn mong mu\u1ed1n g\u1eedi t\u1edbi cho c\u00e1c b\u1ea1n nh\u1eefng ki\u1ebfn th\u1ee9c t\u1ed5ng h\u1ee3p v\u1ec1 l\u00fd thuy\u1ebft v\u00e0 hai d\u1ea1ng b\u00e0i t\u1eadp c\u01a1 b\u1ea3n. Ch\u00fac c\u00e1c b\u1ea1n h\u1ecdc t\u1eadp<\/a> t\u1ed1t!<\/p>\n\n\n\n <\/p>\n\n\n\n V\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 \u0111\u01b0\u1eddng tr\u00f2n<\/p>\n\n\n\n V\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a hai \u0111\u01b0\u1eddng tr\u00f2n<\/p>\n\n\n\n \u0110\u01b0\u1eddng tr\u00f2n ngo\u1ea1i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n n\u1ed9i ti\u1ebfp \u2013 N\u00e2ng cao k\u1ef9 n\u0103ng To\u00e1n<\/p>\n\n\n\n G<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":" Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn B\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y, Vietlearn s\u1ebd t\u1ed5ng h\u1ee3p c\u00e1c ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n v\u1ec1 t\u00ednh ch\u1ea5t c\u1ee7a hai ti\u1ebfp tuy\u1ebfn c\u1eaft nhau m\u1ed9t c\u00e1ch d\u1ec5 hi\u1ec3u v\u00e0 kh\u00e1i qu\u00e1t nh\u1ea5t cho c\u00e1c b\u1ea1n. Bao g\u1ed3m c\u00e1c c\u00f4ng th\u1ee9c, \u0111\u1ecbnh l\u00fd c\u1ea7n thi\u1ebft v\u00e0 \u0111\u1eb7c bi\u1ec7t l\u00e0 m\u1ed9t s\u1ed1 d\u1ea1ng […]<\/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":[9,4],"tags":[],"class_list":["post-1119","post","type-post","status-publish","format-standard","hentry","category-toan-hoc","category-trung-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1119","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=1119"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1119\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=1119"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=1119"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=1119"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}