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{"id":30235,"date":"2018-05-13T14:56:19","date_gmt":"2018-05-13T07:56:19","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=30235"},"modified":"2018-05-13T14:56:19","modified_gmt":"2018-05-13T07:56:19","slug":"hinh-hoc-chuong-2-bai-4-hai-ma%cc%a3t-pha%cc%89ng-song-song","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-4-hai-ma%cc%a3t-pha%cc%89ng-song-song\/","title":{"rendered":"H\u00ecnh H\u1ecdc – Ch\u01b0\u01a1ng 2 – B\u00e0i 4: Hai m\u0103\u0323t ph\u0103\u0309ng song song"},"content":{"rendered":"

B\u00e0i 1 (trang 71 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Trong m\u1eb7t ph\u1eb3ng (\u03b1) cho h\u00ecnh b\u00ecnh h\u00e0nh ABCD. Qua A, B, C, D l\u1ea7n l\u01b0\u1ee3t v\u1ebd b\u1ed1n \u0111\u01b0\u1eddng th\u1eb3ng a, b, c, d song song v\u1edbi nhau v\u00e0 kh\u00f4ng n\u1eb1m tr\u00ean (\u03b1). Tr\u00ean a, b v\u00e0 c l\u1ea7n l\u01b0\u1ee3t l\u1ea5y ba \u0111i\u1ec3m A\u2019, B\u2019 v\u00e0 C\u2019 t\u00f9y \u00fd.<\/p>\n

a) H\u00e3y x\u00e1c \u0111\u1ecbnh giao \u0111i\u1ec3m D\u2019 c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng d v\u1edbi m\u1eb7t ph\u1eb3ng (A\u2019B\u2019C\u2019).<\/p>\n

b) Ch\u1ee9ng minh A\u2019B\u2019C\u2019D\u2019 l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh.<\/p>\n

\"\"<\/p>\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n

a) X\u00e1c \u0111\u1ecbnh giao \u0111i\u1ec3m D\u2019 c\u1ee7a d v\u1edbi mp(A\u2019B\u2019C\u2019)<\/p>\n

\"\"<\/p>\n

=>mp(ABB\u2019A\u2019) \/\/ mp(CDD\u2019C\u2019) m\u00e0 mp(A\u2019B\u2019C\u2019) c\u1eaft mp(ABB\u2019A\u2019), c\u1eaft mp(CDD\u2019C\u2019) theo giao tuy\u1ebfn C\u2019D\u2019 \/\/ A\u2019B\u2019.<\/p>\n

V\u1eady mp(A\u2019B\u2019C\u2019) c\u1eaft d t\u1ea1i D\u2019 sao cho C\u2019D\u2019 \/\/ A\u2019B\u2019 (1)<\/p>\n

b) Ch\u1ee9ng minh A\u2019B\u2019C\u2019D\u2019 l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh<\/p>\n

Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1, ta c\u00f3 B\u2019C\u2019 \/\/ A\u2019D\u2019 (2)<\/p>\n

*T\u1eeb (1) v\u00e0 (2)=>A\u2019B\u2019C\u2019D\u2019 l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh (\u0111pcm).<\/p>\n

B\u00e0i 2 (trang 71 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh l\u0103ng tr\u1ee5 tam gi\u00e1c ABC.A\u2019B\u2019C\u2019. G\u1ecdi M v\u00e0 M\u2019 l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh BC v\u00e0 B\u2019C\u2019.<\/p>\n

a) Ch\u1ee9ng minh r\u1eb1ng AM song song v\u1edbi A\u2019M\u2019.<\/p>\n

b) T\u00ecm giao \u0111i\u1ec3m c\u1ee7a m\u1eb7t ph\u1eb3ng (A\u2019B\u2019C\u2019) v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng A\u2019M.<\/p>\n

c) T\u00ecm giao tuy\u1ebfn d c\u1ee7a hai m\u1eb7t ph\u1eb3ng (AB\u2019C\u2019) v\u00e0 (BA\u2019C\u2019).<\/p>\n

d) T\u00ecm giao \u0111i\u1ec3m G c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng d v\u1edbi mp(AMA\u2019). Ch\u1ee9ng minh G l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c AB\u2019C\u2019.<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

B\u00e0i 3 (trang 71 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh h\u1ed9p ABCD.A\u2019B\u2019C\u2019D\u2019.<\/p>\n

a) Ch\u1ee9ng minh r\u1eb1ng hai m\u1eb7t ph\u1eb3ng (BDA\u2019) v\u00e0 (B\u2019D\u2019C) song song v\u1edbi nhau.<\/p>\n

b) Ch\u1ee9ng minh r\u1eb1ng \u0111\u01b0\u1eddng ch\u00e9o AC\u2019 \u0111i qua tr\u1ecdng t\u00e2m G1<\/sub>\u00a0v\u00e0 G2<\/sub>\u00a0l\u1ea7n l\u01b0\u1ee3t c\u1ee7a hai tam gi\u00e1c BDA\u2019 v\u00e0 B\u2019D\u2019C.<\/p>\n

c) Ch\u1ee9ng minh G1<\/sub>\u00a0v\u00e0 G2<\/sub>\u00a0chia \u0111o\u1ea1n AC\u2019 th\u00e0nh ba ph\u1ea7n b\u1eb1ng nhau.<\/p>\n

d) G\u1ecdi O v\u00e0 I l\u1ea7n l\u01b0\u1ee3t l\u00e0 t\u00e2m c\u00e1c h\u00ecnh b\u00ecnh h\u00e0nh ABCD v\u00e0 \u0394A\u2019C\u2019C. X\u00e1c \u0111\u1ecbnh thi\u1ebft di\u1ec7n c\u1ee7a m\u1eb7t ph\u1eb3ng (A\u2019IO) v\u1edbi h\u00ecnh h\u1ed9p \u0111\u00e3 cho.<\/p>\n

\"\"<\/p>\n

L\u1eddi gi\u1ea3i:<\/b><\/p>\n

A\u2019B \/\/ D\u2019C v\u00e0 D\u2019C \u2282 (B\u2019D\u2019C) => A\u2019B \/\/ (B\u2019D\u2019C)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(1)<\/p>\n

BD \/\/ B\u2019D\u2019 v\u00e0 B\u2019D\u2019 \u2282 (B\u2019D\u2019C) => BD \/\/ (B\u2019D\u2019C)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(2)<\/p>\n

A\u2019B \u2282 (BDA\u2019) v\u00e0 BD \u2282 (BDA\u2019)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(3)<\/p>\n

T\u1eeb (1), (2), (3) suy ra : (BDA\u2019) \/\/ (B\u2019D\u2019C).<\/p>\n

b) G\u1ecdi O l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng ch\u00e9o AC, BD c\u1ee7a h\u00ecnh b\u00ecnh b\u00ecnh h\u00e0nh ABCD, ta c\u00f3 A\u2019O \u2282 (A\u2019ACC\u2019). Trong m\u1eb7t ph\u1eb3ng (A\u2019ACC\u2019) hai \u0111\u01b0\u1eddng th\u1eb3ng A\u2019O v\u00e0 AC\u2019 c\u1eaft nhau t\u1ea1i \u0111i\u1ec3m G1<\/sub>, G1<\/sub>\u00a0\u2208 A\u2019O v\u00e0 A\u2019O \u2282 (BDA\u2019)=> G1<\/sub>\u2208 (BDA\u2019),G1<\/sub>\u00a0\u2208 AC\u2019<\/p>\n

V\u1eady G1<\/sub>\u00a0\u2208 AC\u2019 \u2229 (BDA\u2019)<\/p>\n

T\u1ee9 gi\u00e1c ACC\u2019A\u2019 l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh, giao \u0111i\u1ec3m I c\u1ee7a hai \u0111\u01b0\u1eddng ch\u00e9o A\u2019C v\u00e0 AC\u2019 l\u00e0 trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng.<\/p>\n

X\u00e9t tam gi\u00e1c AA\u2019C, c\u00e1c trung tuy\u1ebfn A\u2019O v\u00e0 AI c\u1eaft nhau t\u1ea1i G1<\/sub>. V\u1eady G1<\/sub>\u00a0l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a \u0394AA\u2019C cho ta OG1<\/sub>\/OA’ = 1\/3 , A\u2019O c\u0169ng l\u00e0 trung tuy\u1ebfn c\u1ee7a \u0394BDA\u2019 n\u00ean t\u1ec9 s\u1ed1 OG1<\/sub>\/OA’ = 1\/3 ch\u1ee9ng t\u1ecf G1 l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c BDA\u2019.<\/p>\n

Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 \u0111\u1ed1i v\u1edbi \u0111i\u1ec3m G2<\/sub>.<\/p>\n

c) *V\u00ec G1<\/sub>\u00a0l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a \u0394AA\u2019C n\u00ean AG1<\/sub>\/AI = 2\/3 .<\/p>\n

V\u00ec I l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AC\u2019 n\u00ean AI = 1\/2.AC\u2019<\/p>\n

T\u1eeb c\u00e1c k\u1ebft qu\u1ea3 n\u00e0y, ta c\u00f3 : AG1<\/sub>\u00a0= 1\/3.AC\u2019<\/p>\n

*Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 ta c\u00f3 : C\u2019G2<\/sub>\u00a0= 1\/3.AC\u2019<\/p>\n

Suy ra : AG1<\/sub>\u00a0= GG2<\/sub>\u00a0= G2<\/sub>C\u2019 = 1\/3.AC\u2019.<\/p>\n

d) Thi\u1ebft di\u1ec7n ch\u00ednh l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh AA\u2019C\u2019C.<\/p>\n

B\u00e0i 4 (trang 71 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh ch\u00f3p S. ABCD. G\u1ecdi A1<\/sub>\u00a0l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh SA v\u00e0 A2<\/sub>\u00a0l\u00e0 trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n AA1<\/sub>. G\u1ecdi (\u03b1) v\u00e0 (\u03b2) l\u00e0 hai m\u1eb7t ph\u1eb3ng song song v\u1edbi m\u1eb7t ph\u1eb3ng (ABCD) v\u00e0 l\u1ea7n l\u01b0\u1ee3t \u0111i qua A1<\/sub>, A2<\/sub>. M\u1eb7t ph\u1eb3ng (\u03b1) c\u1eaft c\u00e1c c\u1ea1nh SB, SC, SD l\u1ea7n l\u01b0\u1ee3t t\u1ea1i B1<\/sub>, C1<\/sub>, D1<\/sub>\u00a0. M\u1eb7t ph\u1eb3ng (\u03b2) c\u1eaft c\u00e1c c\u1ea1nh SB, SC, SD l\u1ea7n l\u01b0\u1ee3t t\u1ea1i B2<\/sub>, C2<\/sub>, D2<\/sub>. Ch\u1ee9ng minh:<\/p>\n

a) B1<\/sub>, C1<\/sub>, D1<\/sub>\u00a0l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh SB, SC, SD.<\/p>\n

b) B1<\/sub>B2<\/sub>\u00a0= B2<\/sub>B, C1<\/sub>C2<\/sub>\u00a0= C2<\/sub>C, D1D2<\/sub>\u00a0= D2<\/sub>D.<\/p>\n

c) Ch\u1ec9 ra c\u00e1c h\u00ecnh ch\u00f3p c\u1ee5t c\u00f3 m\u1ed9t \u0111\u00e1y l\u00e0 t\u1ee9 gi\u00e1c ABCD.<\/p>\n

\"\"<\/p>\n

L\u1eddi gi\u1ea3i<\/strong><\/p>\n

a) Ch\u1ee9ng minh B1<\/sub>, C1<\/sub>, D1<\/sub>\u00a0l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh SB, SC, SD<\/p>\n

Ta c\u00f3:<\/p>\n

\"\"<\/p>\n

=>A1<\/sub>B1<\/sub>\u00a0l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a tam gi\u00e1c SAB.<\/p>\n

=> B1<\/sub>\u00a0l\u00e0 trung \u0111i\u1ec3m c\u1ee7a SB (\u0111pcm)<\/p>\n

*Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 ta c\u0169ng \u0111\u01b0\u1ee3c:<\/p>\n

\u2022 C1<\/sub>\u00a0l\u00e0 trung \u0111i\u1ec3m c\u1ee7a SC.<\/p>\n

\u2022 D1<\/sub>\u00a0l\u00e0 trung \u0111i\u1ec3m c\u1ee7a SD.<\/p>\n

b) Ch\u1ee9ng minh B1<\/sub>B2<\/sub>\u00a0= B2<\/sub>B, C1<\/sub>C2<\/sub>\u00a0= C2C, D1<\/sub>D2<\/sub>\u00a0= D2<\/sub>D.<\/p>\n

\"\"<\/p>\n

=>A2<\/sub>B2<\/sub>\u00a0l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang A1<\/sub>B1<\/sub>BA<\/p>\n

=> B2<\/sub>\u00a0l\u00e0 trung \u0111i\u1ec3m c\u1ee7a B1<\/sub>B<\/p>\n

=> B1<\/sub>B2<\/sub>\u00a0= B2<\/sub>B (\u0111pcm)<\/p>\n

*Ch\u1ee9ng minh t\u01b0\u01a1ng t\u1ef1 ta c\u0169ng \u0111\u01b0\u1ee3c:<\/p>\n

\u2022 C2<\/sub>\u00a0l\u00e0 trung \u0111i\u1ec3m c\u1ee7a C1<\/sub>C2<\/sub>\u00a0=> C1<\/sub>C2<\/sub>\u00a0= C2<\/sub>C<\/p>\n

\u2022 D2<\/sub>\u00a0l\u00e0 trung \u0111i\u1ec3m c\u1ee7a D1<\/sub>D2<\/sub>\u00a0=> D1<\/sub>D2<\/sub>\u00a0= D2<\/sub>D.<\/p>\n

c) C\u00e1c h\u00ecnh ch\u00f3p c\u1ee5t c\u00f3 m\u1ed9t \u0111\u00e1y l\u00e0 t\u1ee9 gi\u00e1c ABCD, \u0111\u00f3 l\u00e0 : A1<\/sub>B1<\/sub>C1<\/sub>D1<\/sub>.ABCD v\u00e0 A2<\/sub>B2<\/sub>C2<\/sub>D2<\/sub>.ABCD<\/p>\n","protected":false},"excerpt":{"rendered":"

B\u00e0i 1 (trang 71 SGK H\u00ecnh h\u1ecdc 11):\u00a0Trong m\u1eb7t ph\u1eb3ng (\u03b1) cho h\u00ecnh b\u00ecnh h\u00e0nh ABCD. Qua A, B, C, D l\u1ea7n l\u01b0\u1ee3t v\u1ebd b\u1ed1n \u0111\u01b0\u1eddng th\u1eb3ng a, b, c, d song song v\u1edbi nhau v\u00e0 kh\u00f4ng n\u1eb1m tr\u00ean (\u03b1). Tr\u00ean a, b v\u00e0 c l\u1ea7n l\u01b0\u1ee3t l\u1ea5y ba \u0111i\u1ec3m A\u2019, B\u2019 v\u00e0 C\u2019 t\u00f9y […]<\/p>\n","protected":false},"author":3,"featured_media":30237,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1318],"tags":[1464,1463],"yoast_head":"\nH\u00ecnh H\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 4: Hai m\u0103\u0323t ph\u0103\u0309ng song song<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-2-bai-4-hai-ma\u0323t-pha\u0309ng-song-song\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"H\u00ecnh H\u1ecdc - Ch\u01b0\u01a1ng 2 - B\u00e0i 4: Hai m\u0103\u0323t ph\u0103\u0309ng song song\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 1 (trang 71 SGK H\u00ecnh h\u1ecdc 11):\u00a0Trong m\u1eb7t ph\u1eb3ng (\u03b1) cho h\u00ecnh b\u00ecnh h\u00e0nh ABCD. Qua A, B, C, D l\u1ea7n l\u01b0\u1ee3t v\u1ebd b\u1ed1n \u0111\u01b0\u1eddng th\u1eb3ng a, b, c, d song song v\u1edbi nhau v\u00e0 kh\u00f4ng n\u1eb1m tr\u00ean (\u03b1). 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