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{"id":30216,"date":"2018-05-13T14:09:57","date_gmt":"2018-05-13T07:09:57","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=30216"},"modified":"2018-05-13T14:09:57","modified_gmt":"2018-05-13T07:09:57","slug":"hinh-hoc-bai-ta%cc%a3p-on-ta%cc%a3p-chuong-2","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/hinh-hoc-bai-ta%cc%a3p-on-ta%cc%a3p-chuong-2\/","title":{"rendered":"H\u00ecnh H\u1ecdc – Ba\u0300i t\u00e2\u0323p \u00f4n t\u00e2\u0323p ch\u01b0\u01a1ng 2"},"content":{"rendered":"

B\u00e0i 1 (trang 77 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho hai h\u00ecnh thang ABCD v\u00e0 ABEF c\u00f3 chung \u0111\u00e1y l\u1edbn AB v\u00e0 kh\u00f4ng c\u00f9ng n\u1eb1m trong m\u1ed9t m\u1eb7t ph\u1eb3ng.<\/p>\n

a) T\u00ecm giao tuy\u1ebfn c\u1ee7a c\u00e1c m\u1eb7t ph\u1eb3ng sau: (AEC) v\u00e0 (BFD), (BCE) v\u00e0 (ADF).<\/p>\n

b) L\u1ea5y \u0111i\u1ec3m M thu\u1ed9c \u0111o\u1ea1n DF. T\u00ecm giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng AM v\u1edbi m\u1eb7t ph\u1eb3ng (BCE).<\/p>\n

c) Ch\u1ee9ng minh hai \u0111\u01b0\u1eddng th\u1eb3ng AC v\u00e0 BF kh\u00f4ng c\u1eaft nhau.<\/p>\n

\"\"<\/p>\n

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

a) Giao tuy\u1ebfn c\u1ee7a c\u00e1c c\u1eb7p m\u1eb7t ph\u1eb3ng<\/p>\n

*Giao tuy\u1ebfn c\u1ee7a (AEC) v\u00e0 (BFD)<\/p>\n

\u2022 Trong h\u00ecnh thang ABCD, AC c\u1eaft DB t\u1ea1i G, ta c\u00f3:<\/p>\n

\"\"<\/p>\n

T\u01b0\u01a1ng t\u1ef1, AE c\u1eaft BF t\u1ea1i H,<\/p>\n

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

V\u1eady GH = (AEC) \u2229 (BFD)<\/p>\n

*Giao tuy\u1ebfn c\u1ee7a (BCE) v\u00e0 (ADF)<\/p>\n

Trong h\u00ecnh thang ABCD, BC c\u1eaft AD t\u1ea1i I, ta c\u00f3: I \u2208 (BCE) \u2229 (ADF)<\/p>\n

Trong h\u00ecnh thang ABEF, BE c\u1eaft AF t\u1ea1i K, ta c\u00f3: K \u2208 (BCE) \u2229 (ADF)<\/p>\n

V\u1eady IK = (BCE) \u2229 (ADF)<\/p>\n

b) Giao \u0111i\u1ec3m c\u1ee7a AM v\u1edbi mp(BCE)<\/p>\n

*Trong mp(ADF), AM c\u1eaft PQ t\u1ea1i N, ta c\u00f3:<\/p>\n

N \u2208AM<\/p>\n

N \u2208 PQ (BCE) N \u2208 (BCE)<\/p>\n

V\u1eady N = AM \u2229 (BCE)<\/p>\n

c) Ch\u1ee9ng minh AC v\u00e0 BF kh\u00f4ng c\u1eaft nhau<\/p>\n

*Gi\u1ea3 s\u1eed AC v\u00e0 BF c\u1eaft nhau t\u1ea1i R, ta c\u00f3 :<\/p>\n

\"\"<\/p>\n

=> AC, BF, AB \u0111\u1ed3ng qui t\u1ea1i R :v\u00f4 l\u00ed !<\/p>\n

V\u1eady AC v\u00e0 BF kh\u00f4ng c\u1eaft nhau.<\/p>\n

B\u00e0i 2 (trang 77 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y ABCD l\u00e0 m\u1ed9t h\u00ecnh b\u00ecnh h\u00e0nh. G\u1ecdi M, N, P theo th\u1ee9 t\u1ef1 l\u00e0 trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n th\u1eb3ng SA, BC, CD. T\u00ecm thi\u1ebft di\u1ec7n c\u1ee7a h\u00ecnh ch\u00f3p khi c\u1eaft b\u1edfi m\u1eb7t ph\u1eb3ng (MNP). G\u1ecdi O l\u00e0 giao \u0111i\u1ec3m hai \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh ABCD, h\u00e3y t\u00ecm giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng SO v\u1edbi m\u1eb7t ph\u1eb3ng (MNP).<\/p>\n

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

\"\"<\/p>\n

a) T\u00ecm ti\u1ebft di\u1ec7n :<\/p>\n

Trong mp(ABCD), g\u1ecdi F = AD \u2229 PN v\u00e0 E = AB \u2229 PN<\/p>\n

Trong mp(SAD), g\u1ecdi Q = ME \u2229 SD v\u00e0 trong mp(SAB), g\u1ecdi R = MF \u2229 SB<\/p>\n

N\u1ed1i PQ, NR ta \u0111\u01b0\u1ee3c c\u00e1c \u0111o\u1ea1n giao tuy\u1ebfn c\u1ee7a mp(MNP) v\u1edbi c\u00e1c m\u1eb7t b\u00ean v\u00e0 m\u1eb7t \u0111\u00e1y c\u1ee7a h\u00ecnh ch\u00f3p l\u00e0 MQ, QP, PN, NR, RM<\/p>\n

C\u00e1c \u0111o\u1ea1n giao tuy\u1ebfn n\u00e0y kh\u00e9p k\u00edn t\u1ea1o th\u00e0nh thi\u1ebft di\u1ec7n l\u00e0 ng\u0169 gi\u00e1c MQPNR.<\/p>\n

b) T\u00ecm SO \u2229 (MNP). G\u1ecdi H l\u00e0 giao \u0111i\u1ec3m c\u1ee7a AC v\u00e0 PN Trong (SBD), SO \u2229 MH = I<\/p>\n

\"\"<\/p>\n

V\u1eady H = SO \u2229 (MNP)<\/p>\n

B\u00e0i 3 (trang 77 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh ch\u00f3p \u0111\u1ec9nh S c\u00f3 \u0111\u00e1y l\u00e0 h\u00ecnh thang ABCD v\u1edbi AB l\u00e0 \u0111\u00e1y l\u1edbn. G\u1ecdi M, N theo th\u1ee9 t\u1ef1 l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh SB v\u00e0 SC.<\/p>\n

a) T\u00ecm giao tuy\u1ebfn c\u1ee7a hai m\u1eb7t ph\u1eb3ng (SAD) v\u00e0 (SBC)<\/p>\n

b) T\u00ecm giap \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng SD v\u1edbi m\u1eb7t ph\u1eb3ng (AMN)<\/p>\n

c) T\u00ecm thi\u1ebft di\u1ec7n c\u1ee7a h\u00ecnh ch\u00f3p S.ABCD c\u1eaft b\u1edfi m\u1eb7t ph\u1eb3ng (AMN)<\/p>\n

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

\"\"<\/p>\n

a) T\u00ecm (SAD) \u2229 (SBC)<\/p>\n

G\u1ecdi E= AD \u2229 BC. Ta c\u00f3:<\/p>\n

\"\"<\/p>\n

Do \u0111\u00f3 E \u2208 (SAD) \u2229 (SBC). M\u00e0 S \u2208 (SAD) \u2229 (SBC). N\u00ean SE = (SAD) \u2229 (SBC)<\/p>\n

b) T\u00ecm SD \u2229 (AMN)<\/p>\n

\"\"<\/p>\n

Trong mp(SBE), g\u1ecdi F = MN \u2229 SE => (AMN) = (AMF)<\/p>\n

Trong mp(SAE), AF \u2229 SD = P<\/p>\n

\"\"<\/p>\n

c) T\u00ecm thi\u1ebft di\u1ec7n v\u1edbi mp(AMN):<\/p>\n

M\u1eb7t ph\u1eb3ng (AMN) c\u1eaft c\u00e1c m\u1eb7t b\u00ean c\u1ee7a h\u00ecnh ch\u00f3p S.ABCD theo c\u00e1c \u0111o\u1ea1n giao tuy\u1ebfn AM, MN, NP, PA.<\/p>\n

B\u00e0i 4 (trang 78 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh b\u00ecnh h\u00e0nh ABCD. Qua A, B, C, D l\u1ea7n l\u01b0\u1ee3t v\u1ebd b\u1ed1n n\u1eeda \u0111\u01b0\u1eddng th\u1eb3ng Ax, By, Cz, Dt \u1edf c\u00f9ng ph\u00eda \u0111\u1ed1i v\u1edbi m\u1eb7t ph\u1eb3ng (ABCD), song song v\u1edbi nhau v\u00e0 kh\u00f4ng n\u1eb1m trong m\u1eb7t ph\u1eb3ng (ABCD). M\u1ed9t m\u1eb7t ph\u1eb3ng (\u03b2) l\u1ea7n l\u01b0\u1ee3t c\u1eaft Ax, By, Cz v\u00e0 Dt t\u1ea1i A\u2019, B\u2019, C\u2019 v\u00e0 D\u2019.<\/p>\n

a) Ch\u1ee9ng minh: m\u1eb7t ph\u1eb3ng (Ax, By) song song v\u1edbi m\u1eb7t ph\u1eb3ng (Cz, Dt)<\/p>\n

b) G\u1ecdi I = AC \u2229 BD, J = A\u2019C\u2019 \u2229 B\u2019D\u2019. Ch\u1ee9ng minh: IJ song song v\u1edbi AA\u2019.<\/p>\n

c) Cho AA\u2019 = a, BB\u2019 = b, CC\u2019 = c. H\u00e3y t\u00ednh DD\u2019.<\/p>\n

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

\"\"<\/p>\n

a) ABDC l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh, n\u00ean:<\/p>\n

AB \/\/ DC (1)<\/p>\n

Theo gi\u1ea3 thi\u1ebft Ax \/\/ Dt (2)<\/p>\n

T\u1eeb (1) v\u00e0 (2) suy ra \u0111pcm.<\/p>\n

b) Do (Ax, By) \/\/ (Cz, Dt) n\u00ean c\u00e1c giao tuy\u1ebfn A\u2019D\u2019 v\u00e0 B\u2019C\u2019 c\u1ee7a c\u00e1c m\u1eb7t ph\u1eb3ng n\u00e0y giao v\u1edbi (\u03b2) song song v\u1edbi nhau, A\u2019B\u2019 \/\/ D\u2019C\u2019.<\/p>\n

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

Suy ra t\u1ee9 gi\u00e1c A\u2019B\u2019C\u2019D\u2019 l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh, cho ta J l\u00e0 trung \u0111i\u1ec3m c\u1ee7a A\u2019C\u2019. Ax \/\/ Cz n\u00ean t\u1ee9 gi\u00e1c ACC\u2019A\u2019 l\u00e0 h\u00ecnh thang, I, J theo th\u1ee9 t\u1ef1 l\u1ea7n l\u01b0\u1ee3t l\u00e0 c\u00e1c trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh b\u00ean AC v\u00e0 A\u2019C\u2019 n\u00ean IJ \/\/ AA\u2019.<\/p>\n

c) V\u00ec IJ l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang ACC\u2019A\u2019 n\u00ean IJ = 1\/2(AA\u2019 + CC\u2019)<\/p>\n

IJ c\u0169ng l\u00e0 \u0111\u01b0\u1eddng trung b\u00ecnh c\u1ee7a h\u00ecnh thang BDD\u2019B\u2019: IJ = 1\/2(BB\u2019 + DD\u2019)<\/p>\n

T\u1eeb \u0111\u00e2y suy ra: DD\u2019 + BB\u2019 = AA\u2019 + CC\u2019 DD\u2019 = a + c \u2013 b<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

B\u00e0i 1 (trang 77 SGK H\u00ecnh h\u1ecdc 11):\u00a0Cho hai h\u00ecnh thang ABCD v\u00e0 ABEF c\u00f3 chung \u0111\u00e1y l\u1edbn AB v\u00e0 kh\u00f4ng c\u00f9ng n\u1eb1m trong m\u1ed9t m\u1eb7t ph\u1eb3ng. a) T\u00ecm giao tuy\u1ebfn c\u1ee7a c\u00e1c m\u1eb7t ph\u1eb3ng sau: (AEC) v\u00e0 (BFD), (BCE) v\u00e0 (ADF). b) L\u1ea5y \u0111i\u1ec3m M thu\u1ed9c \u0111o\u1ea1n DF. T\u00ecm giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng […]<\/p>\n","protected":false},"author":3,"featured_media":30217,"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 - Ba\u0300i t\u00e2\u0323p \u00f4n t\u00e2\u0323p ch\u01b0\u01a1ng 2<\/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-bai-ta\u0323p-on-ta\u0323p-chuong-2\/\" \/>\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 - Ba\u0300i t\u00e2\u0323p \u00f4n t\u00e2\u0323p ch\u01b0\u01a1ng 2\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 1 (trang 77 SGK H\u00ecnh h\u1ecdc 11):\u00a0Cho hai h\u00ecnh thang ABCD v\u00e0 ABEF c\u00f3 chung \u0111\u00e1y l\u1edbn AB v\u00e0 kh\u00f4ng c\u00f9ng n\u1eb1m trong m\u1ed9t m\u1eb7t ph\u1eb3ng. a) T\u00ecm giao tuy\u1ebfn c\u1ee7a c\u00e1c m\u1eb7t ph\u1eb3ng sau: (AEC) v\u00e0 (BFD), (BCE) v\u00e0 (ADF). b) L\u1ea5y \u0111i\u1ec3m M thu\u1ed9c \u0111o\u1ea1n DF. 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