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{"id":30228,"date":"2018-05-13T14:44:14","date_gmt":"2018-05-13T07:44:14","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=30228"},"modified":"2018-05-13T14:44:14","modified_gmt":"2018-05-13T07:44:14","slug":"hinh-hoc-cau-ho%cc%89i-on-ta%cc%a3p-chuong-2","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/hinh-hoc-cau-ho%cc%89i-on-ta%cc%a3p-chuong-2\/","title":{"rendered":"H\u00ecnh H\u1ecdc – C\u00e2u ho\u0309i \u00f4n t\u00e2\u0323p ch\u01b0\u01a1ng 2"},"content":{"rendered":"

B\u00e0i 1 (trang 77 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0H\u00e3y n\u00eau c\u00e1c c\u00e1ch x\u00e1c \u0111\u1ecbnh m\u1eb7t ph\u1eb3ng, k\u00ed hi\u1ec7u m\u1eb7t ph\u1eb3ng.<\/p>\n

\"\"<\/p>\n

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

C\u00f3 3 c\u00e1ch x\u00e1c \u0111\u1ecbnh m\u1eb7t ph\u1eb3ng<\/p>\n

\u2013 M\u1ed9t m\u1eb7t ph\u1eb3ng \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh khi bi\u1ebft ba \u0111i\u1ec3m kh\u00f4ng th\u1eb3ng h\u00e0ng c\u1ee7a n\u00f3.<\/p>\n

\u2013 M\u1ed9t m\u1eb7t ph\u1eb3ng \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh khi bi\u1ebft m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1ed9t \u0111i\u1ec3m n\u1eb1m ngo\u00e0i \u0111\u01b0\u1eddng th\u1eb3ng.<\/p>\n

\u2013 M\u1ed9t m\u1eb7t ph\u1eb3ng \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh khi bi\u1ebft hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau thu\u1ed9c m\u1eb7t ph\u1eb3ng.<\/p>\n

Ngo\u00e0i ra, t\u1eeb \u0111\u1ecbnh ngh\u0129a c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng song song trong kh\u00f4ng gian ta c\u00f2n c\u00f3 c\u00e1ch x\u00e1c \u0111\u1ecbnh.<\/p>\n

\u2013 Hai \u0111\u01b0\u1eddng th\u1eb3ng song song x\u00e1c \u0111\u1ecbnh m\u1ed9t m\u1eb7t ph\u1eb3ng<\/p>\n

B\u00e0i 2 (trang 77 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Th\u1ebf n\u00e0o l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng, \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi m\u1eb7t ph\u1eb3ng, m\u1eb7t ph\u1eb3ng song song v\u1edbi m\u1eb7t ph\u1eb3ng.<\/p>\n

\"\"<\/p>\n

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

– \u0110\u01b0\u1eddng th\u1eb3ng song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng n\u1ebfu ch\u00fang kh\u00f4ng c\u00f3 \u0111i\u1ec3m chung v\u00e0 ch\u00fang c\u00f9ng n\u1eb1m tr\u00ean c\u00f9ng m\u1eb7t ph\u1eb3ng.<\/p>\n

– \u0110\u01b0\u1eddng th\u1eb3ng song song v\u1edbi m\u1eb7t ph\u1eb3ng n\u1ebfu ch\u00fang kh\u00f4ng c\u00f3 \u0111i\u1ec3m chung.<\/p>\n

– M\u1eb7t ph\u1eb3ng song song v\u1edbi m\u1eb7t ph\u1eb3ng n\u1ebfu ch\u00fang kh\u00f4ng c\u00f3 \u0111i\u1ec3m chung.<\/p>\n

B\u00e0i 3 (trang 77 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0N\u00eau ph\u01b0\u01a1ng ph\u00e1p ch\u1ee9ng minh ba \u0111i\u1ec3m th\u1eb3ng h\u00e0ng.<\/p>\n

\"\"<\/p>\n

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

Mu\u1ed1n ch\u1ee9ng minh ba \u0111i\u1ec3m th\u1eb3ng h\u00e0ng ta ch\u1ee9ng minh ba \u0111i\u1ec3m \u0111\u00f3 l\u00e0 ba \u0111i\u1ec3m chung c\u1ee7a hai m\u1eb7t ph\u1eb3ng ph\u00e2n bi\u1ec7t.<\/p>\n

B\u00e0i 4 (trang 77 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0N\u00eau ph\u01b0\u01a1ng ph\u00e1p ch\u1ee9ng minh ba \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy.<\/p>\n

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

\u0110\u1ec3 ch\u1ee9ng minh ba \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u1ed3ng quy, ta ch\u1ee9ng minh:<\/p>\n

\u2013 Ba \u0111\u01b0\u1eddng th\u1eb3ng \u1ea5y kh\u00f4ng \u0111\u1ed3ng ph\u1eb3ng v\u00e0 \u0111\u00f4i m\u1ed9t c\u1eaft nhau.<\/p>\n

\u2013 Ba \u0111\u01b0\u1eddng th\u1eb3ng \u1ea5y l\u00e0 c\u00e1c giao tuy\u1ebfn c\u1ee7a ba m\u1eb7t ph\u1eb3ng ph\u00e2n bi\u1ec7t c\u00f3 m\u1ed9t \u0111i\u1ec3m chung duy nh\u1ea5t.<\/p>\n

B\u00e0i 5 (trang 77 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0N\u00eau ph\u01b0\u01a1ng ph\u00e1p ch\u1ee9ng minh.<\/p>\n

– \u0110\u01b0\u1eddng th\u1eb3ng song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng<\/p>\n

– \u0110\u01b0\u1eddng th\u1eb3ng song song v\u1edbi m\u1eb7t ph\u1eb3ng;<\/p>\n

– M\u1eb7t ph\u1eb3ng song song v\u1edbi m\u1eb7t ph\u1eb3ng.<\/p>\n

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

a) Ch\u1ee9ng minh \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng:<\/p>\n

\u0110\u1ec3 ch\u1ee9ng minh hai \u0111\u01b0\u1eddng th\u1eb3ng song song, ta s\u1eed d\u1ee5ng c\u00e1c \u0111\u1ecbnh l\u00ed.<\/p>\n

– Ba m\u1eb7t ph\u1eb3ng ph\u00e2n bi\u1ec7t \u0111\u00f4i m\u1ed9t c\u1eaft nhau theo ba giao tuy\u1ebfn ph\u00e2n bi\u1ec7t th\u00ec ba giao tuy\u1ebfn \u1ea5y ho\u1eb7c \u0111\u1ed3ng qui ho\u1eb7c \u0111\u00f4i m\u1ed9t song song v\u1edbi nhau.<\/p>\n

– Hai m\u1eb7t ph\u1eb3ng ph\u00e2n bi\u1ec7t l\u1ea7n l\u01b0\u1ee3t ch\u1ee9a hai \u0111\u01b0\u1eddng th\u1eb3ng song song th\u00ec giao tuy\u1ebfn c\u1ee7a ch\u00fang (n\u1ebfu c\u00f3) c\u0169ng song song v\u1edbi hai \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3 ho\u1eb7c tr\u00f9ng v\u1edbi m\u1ed9t trong hai \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3.<\/p>\n

– Hai \u0111\u01b0\u1eddng th\u1eb3ng ph\u00e2n bi\u1ec7t c\u00f9ng song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng th\u1ee9 ba th\u00ec song song v\u1edbi nhau.<\/p>\n

– Cho \u0111\u01b0\u1eddng th\u1eb3ng d song song v\u1edbi m\u1eb7t ph\u1eb3ng (\u03b1). N\u1ebfu m\u1eb7t ph\u1eb3ng (\u03b2) ch\u1ee9a d v\u00e0 c\u1eaft (\u03b1) theo giao tuy\u1ebfn d\u2019 th\u00ec d\u2019 song song v\u1edbi d.<\/p>\n

– Hai m\u1eb7t ph\u1eb3ng ph\u00e2n bi\u1ec7t c\u00f9ng song song v\u1edbi v\u1edbi m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng th\u00ec giao tuy\u1ebfn c\u1ee7a ch\u00fang (n\u1ebfu c\u00f3) c\u0169ng song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3.<\/p>\n

– M\u1ed9t m\u1eb7t ph\u1eb3ng c\u1eaft hai m\u1eb7t ph\u1eb3ng song song cho hai giao tuy\u1ebfn song song.<\/p>\n

– S\u1eed d\u1ee5ng c\u00e1c ph\u01b0\u01a1ng ph\u00e1p c\u1ee7a h\u00ecnh h\u1ecdc ph\u1eb3ng. T\u00ednh ch\u1ea5t \u0111\u01b0\u1eddng trung b\u00ecnh, \u0111\u1ecbnh l\u00ed Ta-l\u00e9t \u0111\u1ea3o, c\u1ea1nh \u0111\u1ed1i h\u00ecnh b\u00ecnh h\u00e0nh\u2026<\/p>\n

– S\u1eed d\u1ee5ng t\u00ednh ch\u1ea5t v\u1ec1 c\u1ea1nh b\u00ean, c\u1ea1nh \u0111\u00e1y c\u1ee7a h\u00ecnh l\u0103ng tr\u1ee5.<\/p>\n

b) Ch\u1ee9ng minh \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi m\u1eb7t ph\u1eb3ng<\/p>\n

– Ch\u1ee9ng minh d song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng d\u2019 n\u1eb1m trong (\u03b1) v\u00e0 d kh\u00f4ng thu\u1ed9c(\u03b1).<\/p>\n

– C\u00f3 hai m\u1eb7t ph\u1eb3ng song song, b\u1ea5t k\u00ec \u0111\u01b0\u1eddng n\u00e0o n\u1eb1m trong hai m\u1eb7t ph\u1eb3ng n\u00e0y c\u0169ng song song v\u1edbi m\u1eb7t ph\u1eb3ng kia.<\/p>\n

c) Ch\u1ee9ng minh m\u1eb7t ph\u1eb3ng song song v\u1edbi m\u1eb7t ph\u1eb3ng<\/p>\n

– Ch\u1ee9ng minh m\u1eb7t ph\u1eb3ng n\u00e0y ch\u1ee9a hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau song song v\u1edbi m\u1eb7t ph\u1eb3ng kia.<\/p>\n

– Ch\u1ee9ng minh hai m\u1eb7t ph\u1eb3ng \u0111\u00f3 c\u00f9ng song song v\u1edbi m\u1eb7t ph\u1eb3ng th\u1ee9 ba.<\/p>\n

B\u00e0i 6 (trang 77 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Ph\u00e1t bi\u1ec3u \u0111\u1ecbnh l\u00ed Ta \u2013 l\u00e9t trong kh\u00f4ng gian.<\/p>\n

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

\u0110\u1ecbnh l\u00ed Ta \u2013 l\u00e9t trong kh\u00f4ng gian:<\/p>\n

– \u0110\u1ecbnh l\u00ed thu\u1eadn\u00a0<\/b>(\u0110\u1ecbnh l\u00ed Ta \u2013 l\u00e9t)<\/p>\n

Ba m\u1eb7t ph\u1eb3ng \u0111\u00f4i m\u1ed9t song song ch\u1eafn tr\u00ean hai c\u00e1t tuy\u1ebfn b\u1ea5t k\u00ec c\u00e1c \u0111o\u1ea1n th\u1eb3ng t\u01b0\u01a1ng \u1ee9ng t\u1ec9 l\u1ec7, ngh\u0129a l\u00e0: Ba m\u1eb7t ph\u1eb3ng song song (P), (Q), (R) c\u1eaft hai \u0111\u01b0\u1eddng th\u1eb3ng a v\u00e0 a’ l\u1ea7n l\u01b0\u1ee3t t\u1ea1i A, B, C v\u00e0 A’, B’, C’:<\/p>\n

Ta c\u00f3 AB\/A’B’= BC\/B’C’ = CA\/C’A’<\/p>\n

– \u0110\u1ecbnh l\u00ed \u0111\u1ea3o<\/b>\u00a0(\u0110\u1ecbnh l\u00ed Ta \u2013 l\u00e9t \u0111\u1ea3o)<\/p>\n

Gi\u1ea3 s\u1eed tr\u00ean hai \u0111\u01b0\u1eddng th\u1eb3ng a v\u00e0 a’ l\u1ea7n l\u01b0\u1ee3t l\u1ea5y hai b\u1ed9 ba \u0111i\u1ec3m (A, B, C) v\u00e0 (A’, B’, C’) sao cho AB\/A’B’= BC\/B’C’ = CA\/C’A’<\/p>\n

Khi \u0111\u00f3 ba \u0111\u01b0\u1eddng th\u1eb3ng AA’, BB’, CC’ c\u00f9ng song song v\u1edbi m\u1ed9t m\u1eb7t ph\u1eb3ng, ngh\u0129a l\u00e0 ba \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00f3 n\u1eb1m tr\u00ean ba m\u1eb7t ph\u1eb3ng song song v\u1edbi nhau.<\/p>\n

B\u00e0i 7 (trang 77 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0N\u00eau c\u00e1ch x\u00e1c \u0111\u1ecbnh thi\u1ebft di\u1ec7n \u0111\u01b0\u1ee3c t\u1ea1o b\u1edfi m\u1ed9t m\u1eb7t ph\u1eb3ng v\u1edbi m\u1ed9t h\u00ecnh ch\u00f3p, h\u00ecnh h\u1ed9p, h\u00ecnh l\u0103ng tr\u1ee5.<\/p>\n

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

\u0110\u1ec3 d\u1ef1ng thi\u1ebft di\u1ec7n t\u1ea1o b\u1edfi m\u1ed9t m\u1eb7t ph\u1eb3ng v\u1edbi h\u00ecnh ch\u00f3p, h\u00ecnh h\u1ed9p, h\u00ecnh l\u0103ng tr\u1ee5, \u0111i\u1ec1u quan tr\u1ecdng l\u00e0 ta ph\u1ea3i x\u00e1c \u0111\u1ecbnh c\u00e1c giao tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng \u1ea5y v\u1edbi c\u00e1c m\u1eb7t c\u1ee7a h\u00ecnh ch\u00f3p, h\u00ecnh h\u1ed9p, h\u00ecnh l\u0103ng tr\u1ee5<\/p>\n

– Tr\u01b0\u1edbc h\u1ebft, ta c\u0169ng c\u1ea7n t\u00ecm giao \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh c\u1ee7a h\u00ecnh ch\u00f3p, h\u00ecnh h\u1ed9p, h\u00ecnh l\u0103ng tr\u1ee5<\/p>\n

– C\u00e1c \u0111o\u1ea1n th\u1eb3ng n\u1ed1i c\u00e1c giao \u0111i\u1ec3m \u1ea5y ch\u00ednh l\u00e0 c\u00e1c c\u1ea1nh c\u1ee7a thi\u1ebft di\u1ec7n<\/p>\n

– Ngo\u00e0i ra c\u1ea7n s\u1eed d\u1ee5ng c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 quan h\u1ec7 song song \u0111\u1ec3 gi\u00fap cho vi\u1ec7c x\u00e1c \u0111\u1ecbnh c\u00e1c giao tuy\u1ebfn \u0111\u01b0\u1ee3c ch\u00ednh x\u00e1c v\u00e0 nhanh g\u1ecdn.<\/p>\n

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

B\u00e0i 1 (trang 77 SGK H\u00ecnh h\u1ecdc 11):\u00a0H\u00e3y n\u00eau c\u00e1c c\u00e1ch x\u00e1c \u0111\u1ecbnh m\u1eb7t ph\u1eb3ng, k\u00ed hi\u1ec7u m\u1eb7t ph\u1eb3ng. L\u1eddi gi\u1ea3i: C\u00f3 3 c\u00e1ch x\u00e1c \u0111\u1ecbnh m\u1eb7t ph\u1eb3ng \u2013 M\u1ed9t m\u1eb7t ph\u1eb3ng \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh khi bi\u1ebft ba \u0111i\u1ec3m kh\u00f4ng th\u1eb3ng h\u00e0ng c\u1ee7a n\u00f3. \u2013 M\u1ed9t m\u1eb7t ph\u1eb3ng \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh khi bi\u1ebft m\u1ed9t \u0111\u01b0\u1eddng […]<\/p>\n","protected":false},"author":3,"featured_media":30229,"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 - C\u00e2u ho\u0309i \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-cau-ho\u0309i-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 - C\u00e2u ho\u0309i \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):\u00a0H\u00e3y n\u00eau c\u00e1c c\u00e1ch x\u00e1c \u0111\u1ecbnh m\u1eb7t ph\u1eb3ng, k\u00ed hi\u1ec7u m\u1eb7t ph\u1eb3ng. 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