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{"id":20754,"date":"2018-03-13T11:38:42","date_gmt":"2018-03-13T04:38:42","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=20754"},"modified":"2018-03-13T11:38:42","modified_gmt":"2018-03-13T04:38:42","slug":"hinh-hoc-chuong-bai-1-khai-niem-ve-khoi-da-dien","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-bai-1-khai-niem-ve-khoi-da-dien\/","title":{"rendered":"H\u00ecnh H\u1ecdc – Ch\u01b0\u01a1ng I – B\u00e0i 1: Kh\u00e1i ni\u1ec7m v\u1ec1 kh\u1ed1i \u0111a di\u1ec7n"},"content":{"rendered":"

B\u00e0i 1 (trang 12 SGK H\u00ecnh h\u1ecdc 12):\u00a0Ch\u1ee9ng minh r\u1eb1ng m\u1ed9t \u0111a di\u1ec7n c\u00f3 c\u00e1c m\u1eb7t l\u00e0 nh\u1eefng tam gi\u00e1c th\u00ec t\u1ed5ng s\u1ed1 c\u00e1c m\u1eb7t c\u1ee7a n\u00f3 ph\u1ea3i l\u00e0 m\u1ed9t s\u1ed1 ch\u1eb5n. Cho v\u00ed d\u1ee5:<\/strong><\/span><\/p>\n

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

*G\u1ecdi a l\u00e0 s\u1ed1 c\u1ea1nh, b l\u00e0 s\u1ed1 m\u1eb7t c\u1ee7a kh\u1ed1i \u0111a di\u1ec7n.<\/p>\n

N\u1ebfu kh\u1ed1i \u0111a di\u1ec7n c\u00f3 c\u00e1c m\u1eb7t l\u00e0 tam gi\u00e1c th\u00ec m\u1ed7i m\u1eb7t c\u00f3 ba c\u1ea1nh. Trong ba c\u1ea1nh \u0111\u00f3 m\u1ed7i c\u1ea1nh l\u1ea7n l\u01b0\u1ee3t l\u00e0 c\u1ea1nh chung c\u1ee7a hai m\u1eb7t.<\/p>\n

Ta c\u00f3 3b = 2a. Ngh\u0129a l\u00e0 b ch\u1eb5n.<\/p>\n

*V\u00ed d\u1ee5: h\u00ecnh 1,2<\/p>\n

\"\"<\/p>\n

B\u00e0i 2 (trang 12 SGK H\u00ecnh h\u1ecdc 12):\u00a0Ch\u1ee9ng minh r\u1eb1ng m\u1ed9t \u0111a di\u1ec7n m\u00e0 m\u1ed7i \u0111\u1ec9nh c\u1ee7a n\u00f3 l\u00e0 \u0111\u1ec9nh chung c\u1ee7a m\u1ed9t s\u1ed1 l\u1ebb m\u1eb7t th\u00ec t\u1ed5ng s\u1ed1 c\u00e1c \u0111\u1ec9nh c\u1ee7a n\u00f3 ph\u1ea3i l\u00e0 m\u1ed9t s\u1ed1 ch\u1eb5n. Cho v\u00ed d\u1ee5.<\/strong><\/span><\/p>\n

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

Cho kh\u1ed1i \u0111a di\u1ec7n G c\u00f3 c\u00e1c \u0111\u1ec9nh l\u00e0 B1<\/sub>, B2<\/sub>,\u2026, Bn<\/sub>\u00a0v\u00e0 g\u1ecdi M1<\/sub>, M2<\/sub>,\u2026, Mn<\/sub>\u00a0l\u1ea7n l\u01b0\u1ee3t l\u00e0 s\u1ed1 c\u00e1c m\u1eb7t c\u1ee7a H nh\u1eadn ch\u00fang l\u00e0m \u0111\u1ec9nh chung. T\u1ed5ng s\u1ed1 c\u00e1c c\u1ea1nh c\u1ee7a G l\u00e0:<\/p>\n

C = (M1<\/sub>\u00a0+ M2<\/sub>\u00a0+ \u2026 + Mn<\/sub>)\/2<\/p>\n

V\u00ec C l\u00e0 s\u1ed1 nguy\u00ean d\u01b0\u01a1ng n\u00ean:<\/p>\n

M1<\/sub>\u00a0+ M2<\/sub>\u00a0+ \u2026 + Mn<\/sub>\u00a0l\u00e0 s\u1ed1 ch\u1eb5n.<\/p>\n

\u0110\u1ed3ng th\u1eddi M1<\/sub>\u00a0,M2<\/sub>\u00a0, …, Mn<\/sub>\u00a0l\u00e0 n s\u1ed1 t\u1ef1 nhi\u00ean l\u1ebb n\u00ean t\u1ed5ng c\u1ee7a ch\u00fang l\u00e0 s\u1ed1 ch\u1eb5n khi n ch\u1eb5n.<\/p>\n

V\u00ed d\u1ee5: H\u00ecnh ch\u00f3p ng\u0169 gi\u00e1c B1<\/sub>B2<\/sub>B3<\/sub>B4<\/sub>B5<\/sub>B6<\/sub>\u00a0c\u00f3: B1<\/sub>\u00a0l\u00e0 \u0111\u1ec9nh chung c\u1ee7a 5 m\u1eb7t b\u00ean. M\u1ed7i \u0111\u1ec9nh B1<\/sub>, B2<\/sub>, B3<\/sub>, B4<\/sub>, B5<\/sub>, B6<\/sub>\u00a0l\u00e0 \u0111\u1ec9nh chung c\u1ee7a ba m\u1eb7t (h\u00ecnh tr\u00ean).<\/p>\n

\"\"<\/p>\n

B\u00e0i 3 (trang 12 SGK H\u00ecnh h\u1ecdc 12):\u00a0Chia m\u1ed9t kh\u1ed1i l\u1eadp ph\u01b0\u01a1ng th\u00e0nh n\u0103m kh\u1ed1i t\u1ee9 di\u1ec7n.<\/strong><\/span><\/p>\n

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

\"\"<\/p>\n

Trong h\u00ecnh b\u00ean, ta c\u00f3 th\u1ec3 chia th\u00e0nh n\u0103m kh\u1ed1i t\u1ee9 di\u1ec7n l\u00e0 AA\u2019D\u2019B\u2019, ABCB\u2019, ADCD\u2019,AD\u2019CB\u2019, CD\u2019C\u2019B\u2019.<\/p>\n

B\u00e0i 4 (trang 12 SGK H\u00ecnh h\u1ecdc 12):\u00a0Chia kh\u1ed1i l\u1eadp ph\u01b0\u01a1ng th\u00e0nh s\u00e1u kh\u1ed1i t\u1ee9 di\u1ec7n b\u1eb1ng nhau.<\/strong><\/span><\/p>\n

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

\"\"<\/p>\n

Trong h\u00ecnh b\u00ean, ta c\u00f3 th\u1ec3 chia th\u00e0nh s\u00e1u kh\u1ed1i t\u1ee9 di\u1ec7n b\u1eb1ng nhau nh\u01b0 sau:<\/p>\n

+Chia kh\u1ed1i l\u1eadp ph\u01b0\u01a1ng ABCD.A1<\/sub>B1<\/sub>C1<\/sub>D1<\/sub>\u00a0th\u00e0nh hai kh\u1ed1i l\u0103ng tr\u1ee5 tam gi\u00e1c b\u1eb1ng nhau: ABD.A1<\/sub>B1<\/sub>D1<\/sub>v\u00e0 BCD.B1<\/sub>C1<\/sub>D1<\/sub>.<\/p>\n

+Ti\u1ebfp \u0111\u00f3, l\u1ea7n l\u01b0\u1ee3t chia kh\u1ed1i l\u0103ng tr\u1ee5 ABD.A1<\/sub>B1<\/sub>D1<\/sub>\u00a0v\u00e0 BCD.B1<\/sub>C1<\/sub>D1<\/sub>\u00a0th\u00e0nh ba t\u1ee9 di\u1ec7n: DABB1<\/sub>, DAA1<\/sub>B1<\/sub>v\u00e0 DCBB1<\/sub>, DCC1<\/sub>B1<\/sub>, DD1<\/sub>C1<\/sub>B1<\/sub>.<\/p>\n

+Ta ch\u1ee9ng minh \u0111\u01b0\u1ee3c c\u00e1c kh\u1ed1i t\u1ee9 di\u1ec7n n\u00e0y b\u1eb1ng nhau nh\u01b0 sau:<\/p>\n

-Hai kh\u1ed1i t\u1ee9 di\u1ec7n DABB1<\/sub>\u00a0v\u00e0 DAA1<\/sub>B1<\/sub>\u00a0b\u1eb1ng nhau v\u00ec ch\u00fang \u0111\u1ed1i x\u1ee9ng nhau qua m\u1eb7t ph\u1eb3ng (DAB1<\/sub>) (1)<\/p>\n

-Hai kh\u1ed1i t\u1ee9 di\u1ec7n DAA1<\/sub>B1<\/sub>\u00a0v\u00e0 DD1<\/sub>A1<\/sub>B1<\/sub>\u00a0b\u1eb1ng nhau v\u00ec ch\u00fang \u0111\u1ed1i x\u1ee9ng nhau qua m\u1eb7t ph\u1eb3ng (B1<\/sub>A1<\/sub>D) (2)<\/p>\n

T\u1eeb (1) v\u00e0 (2) suy ra ba kh\u1ed1i t\u1ee9 di\u1ec7n DABB1<\/sub>, DAA1<\/sub>B1<\/sub>\u00a0v\u00e0 DD1<\/sub>A1<\/sub>B1<\/sub>\u00a0b\u1eb1ng nhau.<\/p>\n

-T\u01b0\u01a1ng t\u1ef1, ba kh\u1ed1i t\u1ee9 di\u1ec7n DCBB1<\/sub>, DCC1<\/sub>B1<\/sub>, DD1<\/sub>C1<\/sub>B1<\/sub>\u00a0c\u0169ng b\u1eb1ng nhau.<\/p>\n

V\u1eady kh\u1ed1i l\u1eadp ph\u01b0\u01a1ng ABCD.A1<\/sub>B1<\/sub>C1<\/sub>D1<\/sub>\u00a0\u0111\u01b0\u1ee3c chia th\u00e0nh s\u00e1u kh\u1ed1i t\u1ee9 di\u1ec7n b\u1eb1ng nhau.<\/p>\n

\"\"<\/p>\n

 <\/p>\n

<\/div>\n

\u00a0<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"

B\u00e0i 1 (trang 12 SGK H\u00ecnh h\u1ecdc 12):\u00a0Ch\u1ee9ng minh r\u1eb1ng m\u1ed9t \u0111a di\u1ec7n c\u00f3 c\u00e1c m\u1eb7t l\u00e0 nh\u1eefng tam gi\u00e1c th\u00ec t\u1ed5ng s\u1ed1 c\u00e1c m\u1eb7t c\u1ee7a n\u00f3 ph\u1ea3i l\u00e0 m\u1ed9t s\u1ed1 ch\u1eb5n. Cho v\u00ed d\u1ee5: L\u1eddi gi\u1ea3i: *G\u1ecdi a l\u00e0 s\u1ed1 c\u1ea1nh, b l\u00e0 s\u1ed1 m\u1eb7t c\u1ee7a kh\u1ed1i \u0111a di\u1ec7n. N\u1ebfu kh\u1ed1i \u0111a di\u1ec7n c\u00f3 […]<\/p>\n","protected":false},"author":3,"featured_media":20758,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1298],"tags":[1377,1356,1355],"yoast_head":"\nH\u00ecnh H\u1ecdc - Ch\u01b0\u01a1ng I - B\u00e0i 1: Kh\u00e1i ni\u1ec7m v\u1ec1 kh\u1ed1i \u0111a di\u1ec7n<\/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-bai-1-khai-niem-ve-khoi-da-dien\/\" \/>\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 I - B\u00e0i 1: Kh\u00e1i ni\u1ec7m v\u1ec1 kh\u1ed1i \u0111a di\u1ec7n\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 1 (trang 12 SGK H\u00ecnh h\u1ecdc 12):\u00a0Ch\u1ee9ng minh r\u1eb1ng m\u1ed9t \u0111a di\u1ec7n c\u00f3 c\u00e1c m\u1eb7t l\u00e0 nh\u1eefng tam gi\u00e1c th\u00ec t\u1ed5ng s\u1ed1 c\u00e1c m\u1eb7t c\u1ee7a n\u00f3 ph\u1ea3i l\u00e0 m\u1ed9t s\u1ed1 ch\u1eb5n. Cho v\u00ed d\u1ee5: L\u1eddi gi\u1ea3i: *G\u1ecdi a l\u00e0 s\u1ed1 c\u1ea1nh, b l\u00e0 s\u1ed1 m\u1eb7t c\u1ee7a kh\u1ed1i \u0111a di\u1ec7n. 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