Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
Trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n<\/a> h\u1ecdc l\u1edbp 9, li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y l\u00e0 b\u00e0i h\u1ecdc quan tr\u1ecdng nh\u1eb1m c\u00f3 ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng \u0111\u1ec3 gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc kh\u00f4ng gian \u0111\u01b0\u1ee3c t\u1ed1t nh\u1ea5t. \u0110\u1ec3 hi\u1ec3u \u0111\u01b0\u1ee3c l\u00fd thuy\u1ebft v\u00e0 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp th\u00f4ng d\u1ee5ng, h\u00e3y c\u00f9ng Vietlearn.org\/ theo d\u00f5i b\u00e0i gi\u1ea3ng sau v\u1edbi c\u00e1c m\u1eb9o \u00f4n luy\u1ec7n hi\u1ec7u qu\u1ea3 hi\u1ec7n nay.<\/p>\n\n\n\n I. L\u00fd thuy\u1ebft v\u1ec1 li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y:<\/p>\n\n\n\n Trong ki\u1ebfn th\u1ee9c to\u00e1n 9 b\u00e0i li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y c\u00f3 2 \u0111\u1ecbnh l\u00fd sau:<\/p>\n\n\n\n \u0110\u1ecbnh l\u00fd 1: \u0110\u1ed1i v\u1edbi 1 \u0111\u01b0\u1eddng tr\u00f2n:<\/p>\n\n\n\n 2 d\u00e2y b\u1eb1ng nhau th\u00ec s\u1ebd c\u00e1ch \u0111\u1ec1u t\u00e2m.<\/p>\n\n\n\n 2 d\u00e2y c\u00e1ch \u0111\u1ec1u v\u1edbi t\u00e2m th\u00ec s\u1ebd b\u1eb1ng nhau.<\/p>\n\n\n\n \u0110\u1ecbnh l\u00fd 2: Trong 1 \u0111\u01b0\u1eddng tr\u00f2n, 2 d\u00e2y c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n s\u1ebd:<\/p>\n\n\n\n D\u00e2y n\u00e0o c\u00f3 \u0111\u1ed9 d\u00e0i l\u1edbn h\u01a1n th\u00ec d\u00e2y \u0111\u00f3 s\u1ebd g\u1ea7n t\u00e2m h\u01a1n.<\/p>\n\n\n\n D\u00e2y n\u00e0o g\u1ea7n v\u1edbi t\u00e2m h\u01a1n th\u00ec d\u00e2y \u0111\u00f3 s\u1ebd l\u1edbn h\u01a1n.<\/p>\n\n\n\n C\u00e1c \u0111\u1ecbnh l\u00fd v\u1ec1 li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y<\/p>\n\n\n\n V\u00ed d\u1ee5 minh h\u1ecda:<\/p>\n\n\n\n X\u00e9t \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O, b\u00e1n k\u00ednh R (O,R) c\u00f3 2 d\u00e2y AB v\u00e0 CD<\/p>\n\n\n\n OH \u22a5 AB t\u1ea1i \u0111i\u1ec3m H (H \u2208 AB)<\/p>\n\n\n\n OK \u22a5 CD t\u1ea1i \u0111i\u1ec3m K (K \u2208 CD)<\/p>\n\n\n\n Khi \u0111\u00f3 ta c\u00f3:<\/p>\n\n\n\n AB = CD \u21d4 OH = OK<\/p>\n\n\n\n AB > CD \u21d4 OH < OK<\/p>\n\n\n\n \u0110\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n<\/p><\/blockquote>\n\n\n\n Trong ch\u01b0\u01a1ng tr\u00ecnh to\u00e1n<\/a> 9 li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y l\u00e0 m\u1ed9t trong nh\u1eefng ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng quan tr\u1ecdng gi\u00fap c\u00e1c em d\u1ec5 d\u00e0ng gi\u1ea3i \u0111\u01b0\u1ee3c nh\u1eefng b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn h\u00ecnh h\u1ecdc kh\u00f4ng gian sau n\u00e0y. \u0110\u1ed1i v\u1edbi b\u00e0i gi\u1ea3ng v\u1ec1 ki\u1ebfn th\u1ee9c n\u00e0y s\u1ebd c\u00f3 nh\u1eefng m\u1eb9o v\u00e0 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp c\u01a1 b\u1ea3n sau gi\u00fap c\u00e1c em d\u1ec5 d\u00e0ng h\u1ec7 th\u1ed1ng h\u00f3a l\u1ea1i ki\u1ebfn th\u1ee9c c\u0169ng nh\u01b0 \u00f4n thi<\/a> \u0111\u01b0\u1ee3c hi\u1ec7u qu\u1ea3 nh\u1ea5t c\u00f3 th\u1ec3.<\/p>\n\n\n\n D\u1ea1ng 1: T\u00ednh to\u00e1n \u0111\u1ed9 d\u00e0i c\u1ee7a \u0111o\u1ea1n th\u1eb3ng v\u00e0 nh\u1eefng y\u1ebfu t\u1ed1 li\u00ean quan.<\/p>\n\n\n\n C\u00e1ch th\u1ee9c gi\u1ea3i:<\/p>\n\n\n\n M\u1ed9t trong nh\u1eefng d\u1ea1ng to\u00e1n quan tr\u1ecdng trong b\u00e0i gi\u1ea3ng n\u00e0y l\u00e0 t\u00ednh to\u00e1n \u0111\u1ed9 d\u00e0i c\u1ee7a \u0111o\u1ea1n th\u1eb3ng v\u00e0 nh\u1eefng y\u1ebfu t\u1ed1 li\u00ean quan gi\u1eefa d\u00e2y c\u0169ng nh\u01b0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y. \u0110\u1ec3 gi\u1ea3i \u0111\u01b0\u1ee3c d\u1ea1ng to\u00e1n n\u00e0y, th\u00f4ng th\u01b0\u1eddng s\u1ebd s\u1eed d\u1ee5ng nh\u1eefng ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n<\/a> sau.<\/p>\n\n\n\n Quan h\u1ec7 vu\u00f4ng g\u00f3c c\u1ee7a \u0111\u01b0\u1eddng k\u00ednh v\u00e0 d\u00e2y:<\/p>\n\n\n\n N\u1ebfu \u0111\u01b0\u1eddng k\u00ednh m\u00e0 vu\u00f4ng g\u00f3c v\u1edbi 1 d\u00e2y trong 1 \u0111\u01b0\u1eddng tr\u00f2n th\u00ec \u0111i qua trung \u0111i\u1ec3m c\u1ee7a d\u00e2y \u0111\u00f3.<\/p>\n\n\n\n N\u1ebfu \u0111\u01b0\u1eddng k\u00ednh m\u00e0 \u0111i qua trung \u0111i\u1ec3m c\u1ee7a 1 d\u00e2y v\u00e0 kh\u00f4ng \u0111i qua t\u00e2m trong 1 \u0111\u01b0\u1eddng tr\u00f2n th\u00ec vu\u00f4ng g\u00f3c v\u1edbi d\u00e2y \u0111\u00f3.<\/p>\n\n\n\n \u00c1p d\u1ee5ng \u0111\u1ecbnh l\u00fd Pitago v\u1ec1 h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng c\u1ee7a tam gi\u00e1c vu\u00f4ng:<\/p>\n\n\n\n Cho tam gi\u00e1c \u0394ABC vu\u00f4ng t\u1ea1i A. Ta c\u00f3: AB\u00b2 + AC\u00b2 = BC\u00b2<\/p>\n\n\n\n D\u1ea1ng to\u00e1n t\u00ednh \u0111\u1ed9 d\u00e0i c\u1ee7a \u0111o\u1ea1n th\u1eb3ng v\u00e0 nh\u1eefng y\u1ebfu t\u1ed1 li\u00ean quan<\/p>\n\n\n\n D\u1ea1ng 2: So s\u00e1nh gi\u1eefa hai \u0111o\u1ea1n th\u1eb3ng<\/p>\n\n\n\n C\u00e1ch th\u1ee9c gi\u1ea3i:<\/p>\n\n\n\n \u0110\u1ed1i v\u1edbi b\u00e0i gi\u1ea3ng v\u1ec1 d\u1ea1ng ki\u1ebfn th\u1ee9c n\u00e0y, so s\u00e1nh gi\u1eefa hai \u0111o\u1ea1n th\u1eb3ng l\u00e0 m\u1ed9t trong nh\u1eefng d\u1ea1ng to\u00e1n c\u01a1 b\u1ea3n, \u0111\u1eb7c bi\u1ec7t l\u00e0 th\u01b0\u1eddng b\u1eaft g\u1eb7p trong nh\u1eefng b\u00e0i ki\u1ec3m tra. Th\u00f4ng th\u01b0\u1eddng \u0111\u1ed1i v\u1edbi d\u1ea1ng to\u00e1n n\u00e0y, \u0111\u1ec3 c\u00f3 th\u1ec3 gi\u1ea3i c\u1ea7n \u00e1p d\u1ee5ng nh\u1eefng ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n<\/a> sau:<\/p>\n\n\n\n \u0110\u1ed1i v\u1edbi 1 \u0111\u01b0\u1eddng tr\u00f2n:<\/p>\n\n\n\n 2 d\u00e2y b\u1eb1ng nhau th\u00ec s\u1ebd c\u00e1ch \u0111\u1ec1u t\u00e2m.<\/p>\n\n\n\n 2 d\u00e2y c\u00e1ch \u0111\u1ec1u v\u1edbi t\u00e2m th\u00ec s\u1ebd b\u1eb1ng nhau.<\/p>\n\n\n\n Trong 1 \u0111\u01b0\u1eddng tr\u00f2n, 2 d\u00e2y c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n s\u1ebd:<\/p>\n\n\n\n D\u00e2y n\u00e0o c\u00f3 \u0111\u1ed9 d\u00e0i l\u1edbn h\u01a1n th\u00ec d\u00e2y \u0111\u00f3 s\u1ebd g\u1ea7n t\u00e2m h\u01a1n.<\/p>\n\n\n\n D\u00e2y n\u00e0o g\u1ea7n v\u1edbi t\u00e2m h\u01a1n th\u00ec d\u00e2y \u0111\u00f3 s\u1ebd l\u1edbn h\u01a1n.<\/p>\n\n\n\n Ch\u1ee9ng minh 2 tam gi\u00e1c b\u1eb1ng nhau v\u00e0 \u00e1p d\u1ee5ng quan h\u1ec7 gi\u1eefa nh\u1eefng y\u1ebfu t\u1ed1 trong tam gi\u00e1c nh\u01b0: Tr\u01b0\u1eddng h\u1ee3p c\u1ea1nh \u2013 c\u1ea1nh \u2013 c\u1ea1nh, tr\u01b0\u1eddng h\u1ee3p c\u1ea1nh \u2013 g\u00f3c \u2013 c\u1ea1nh, hay tr\u01b0\u1eddng h\u1ee3p g\u00f3c \u2013 c\u1ea1nh \u2013 g\u00f3c.<\/p>\n\n\n\n D\u1ea1ng to\u00e1n so s\u00e1nh gi\u1eefa hai \u0111o\u1ea1n th\u1eb3ng<\/p>\n\n\n\n II. B\u00e0i t\u1eadp v\u1ec1 li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y:<\/p>\n\n\n\n \u0110\u1ec3 h\u1ec7 th\u1ed1ng h\u00f3a l\u1ea1i ki\u1ebfn th\u1ee9c l\u00fd thuy\u1ebft v\u1ec1 v\u1ec1 m\u1ed7i li\u00ean quan gi\u1eefa d\u00e2y c\u0169ng nh\u01b0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m t\u1edbi d\u00e2y v\u00e0 \u00e1p d\u1ee5ng c\u00e1c d\u1ea1ng to\u00e1n li\u00ean quan \u0111\u1ebfn b\u00e0i h\u1ecdc n\u00e0y. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp c\u01a1 b\u1ea3n v\u1ec1 to\u00e1n 9 b\u00e0i li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y trong s\u00e1ch gi\u00e1o khoa.<\/p>\n\n\n\n B\u00e0i t\u1eadp 1: (B\u00e0i 12\/SGK T\u1eadp 1, To\u00e1n 9, trang 106)<\/p>\n\n\n\n Cho 1 \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O v\u1edbi b\u00e1n k\u00ednh R b\u1eb1ng 5cm v\u00e0 d\u00e2y AB b\u1eb1ng 8cm.<\/p>\n\n\n\n T\u00ednh \u0111\u1ed9 d\u00e0i kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m O t\u1edbi d\u00e2y AB.<\/p>\n\n\n\n G\u1ecdi I l\u00e0 1 \u0111i\u1ec3m thu\u1ed9c d\u00e2y cung AB sao cho AI b\u1eb1ng 1cm. K\u1ebb 1 d\u00e2y CD \u0111i qua \u0111i\u1ec3m I v\u00e0 n\u1eb1m vu\u00f4ng g\u00f3c v\u1edbi d\u00e2y AB. Ch\u1ee9ng minh r\u1eb1ng AB = CD.<\/p>\n\n\n\n B\u00e0i t\u1eadp 2: (B\u00e0i 13\/SGK T\u1eadp 1, To\u00e1n 9, trang 106)<\/p>\n\n\n\n Cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O, b\u00e1n k\u00ednh R (O,R) c\u00f3 d\u00e2y AB v\u00e0 d\u00e2y CD b\u1eb1ng nhau, tia AB v\u00e0 CD c\u1eaft nhau t\u1ea1i E v\u00e0 n\u1eb1m b\u00ean ngo\u00e0i c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n. G\u1ecdi \u0111i\u1ec3m H v\u00e0 \u0111i\u1ec3m K l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a d\u00e2y AB v\u00e0 d\u00e2y CD. Ch\u1ee9ng minh r\u1eb1ng:<\/p>\n\n\n\n EH = EK.<\/p>\n\n\n\n AE = CE.<\/p>\n\n\n\n B\u00e0i t\u1eadp 3: (B\u00e0i 14\/SGK T\u1eadp 1, To\u00e1n 9, trang 106)<\/p>\n\n\n\n Cho \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O c\u00f3 b\u00e1n k\u00ednh R b\u1eb1ng 25cm v\u00e0 d\u00e2y AB c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng 40cm. V\u1ebd 1 d\u00e2y CD song song v\u1edbi d\u00e2y AB v\u00e0 kho\u1ea3ng c\u00e1ch \u0111\u1ebfn AB l\u00e0 22cm. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ee7a d\u00e2y CD.<\/p>\n\n\n\n B\u00e0i t\u1eadp v\u1ec1 li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y<\/p>\n\n\n\n B\u00e0i gi\u1ea3ng tr\u00ean \u0111\u00e3 cung c\u1ea5p ki\u1ebfn th\u1ee9c v\u1ec1 li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y, c\u0169ng nh\u01b0 l\u00fd thuy\u1ebft v\u00e0 c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp th\u01b0\u1eddng g\u1eb7p. Hy v\u1ecdng \u0111\u00e2y s\u1ebd l\u00e0 nh\u1eefng th\u00f4ng tin b\u1ed5 \u00edch d\u00e0nh cho c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a> v\u00e0 qu\u00fd ph\u1ee5 huynh c\u00f3 nhu c\u1ea7u gi\u1ea3ng d\u1ea1y v\u00e0 \u00f4n t\u1eadp cho con em c\u1ee7a m\u00ecnh. \u0110\u1eebng qu\u00ean th\u01b0\u1eddng xuy\u00ean truy c\u1eadp Vietlearn.org\/ \u0111\u1ec3 c\u1eadp nh\u1eadt th\u00eam nh\u1eefng ki\u1ebfn th\u1ee9c m\u00f4n h\u1ecdc kh\u00e1c nh\u00e9!<\/p>\n\n\n\n T\u00ecm hi\u1ec3u th\u00eam:<\/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<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":" Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn Trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n h\u1ecdc l\u1edbp 9, li\u00ean h\u1ec7 gi\u1eefa d\u00e2y v\u00e0 kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn d\u00e2y l\u00e0 b\u00e0i h\u1ecdc quan tr\u1ecdng nh\u1eb1m c\u00f3 ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng \u0111\u1ec3 gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc kh\u00f4ng gian \u0111\u01b0\u1ee3c t\u1ed1t nh\u1ea5t. \u0110\u1ec3 hi\u1ec3u \u0111\u01b0\u1ee3c l\u00fd thuy\u1ebft v\u00e0 c\u00e1c 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-995","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\/995","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=995"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/995\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=995"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=995"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=995"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}