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{"id":20661,"date":"2018-03-13T11:13:05","date_gmt":"2018-03-13T04:13:05","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=20661"},"modified":"2018-03-13T11:13:05","modified_gmt":"2018-03-13T04:13:05","slug":"hinh-hoc-chuong-khoi-da-dien-tap","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-khoi-da-dien-tap\/","title":{"rendered":"H\u00ecnh H\u1ecdc – Ch\u01b0\u01a1ng I: Kh\u1ed1i \u0111a di\u1ec7n – \u00d4n t\u1eadp"},"content":{"rendered":"

B\u00e0i 1 (trang 26 SGK H\u00ecnh h\u1ecdc 12):\u00a0C\u00e1c \u0111\u1ec9nh, c\u1ea1nh, m\u1eb7t c\u1ee7a m\u1ed9t \u0111a di\u1ec7n ph\u1ea3i th\u1ecfa m\u00e3n nh\u1eefng t\u00ednh ch\u1ea5t n\u00e0o?<\/strong><\/span><\/p>\n

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

C\u00e1c \u0111\u1ec9nh, c\u1ea1nh, m\u1eb7t c\u1ee7a m\u1ed9t \u0111a di\u1ec7n ph\u1ea3i th\u1ecfa m\u00e3n nh\u1eefng t\u00ednh ch\u1ea5t:<\/p>\n

– M\u1ed7i \u0111\u1ec9nh l\u00e0 \u0111\u1ec9nh chung c\u1ee7a \u00edt nh\u1ea5t ba c\u1ea1nh, ba m\u1eb7t;<\/p>\n

– M\u1ed7i c\u1ea1nh l\u00e0 c\u1ea1nh chung c\u1ee7a \u0111\u00fang hai m\u1eb7t;<\/p>\n

– Hai m\u1eb7t b\u1ea5t k\u00ec ho\u1eb7c kh\u00f4ng c\u00f3 \u0111i\u1ec3m chung, ho\u1eb7c c\u00f3 m\u1ed9t \u0111\u1ec9nh chung, ho\u1eb7c c\u00f3 \u0111\u00fang m\u1ed9t c\u1ea1nh chung.<\/p>\n

B\u00e0i 2 (trang 26 SGK H\u00ecnh h\u1ecdc 12):\u00a0T\u00ecm m\u1ed9t h\u00ecnh t\u1ea1o b\u1edfi c\u00e1c \u0111a gi\u00e1c nh\u01b0ng kh\u00f4ng ph\u1ea3i l\u00e0 m\u1ed9t \u0111a di\u1ec7n<\/strong><\/span><\/p>\n

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

\"\"<\/p>\n

H\u00ecnh tr\u00ean kh\u00f4ng ph\u1ea3i l\u00e0 \u0111a di\u1ec7n v\u00ec c\u00f3 1 c\u1ea1nh l\u00e0 c\u1ea1nh chung c\u1ee7a 4 m\u1eb7t ph\u1eb3ng.<\/p>\n

B\u00e0i 3 (trang 26 SGK H\u00ecnh h\u1ecdc 12):\u00a0Th\u1ebf n\u00e0o l\u00e0 m\u1ed9t kh\u1ed1i \u0111a di\u1ec7n l\u1ed3i. T\u00ecm v\u00ed d\u1ee5 trong th\u1ef1c t\u1ebf m\u00f4 t\u1ea3 m\u1ed9t kh\u1ed1i \u0111a di\u1ec7n l\u1ed3i, m\u1ed9t kh\u1ed1i \u0111a di\u1ec7n kh\u00f4ng l\u1ed3i.<\/strong><\/span><\/p>\n

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

V\u1edbi hai \u0111i\u1ec3m M v\u00e0 N thu\u1ed9c kh\u1ed1i \u0111a di\u1ec7n th\u00ec m\u1ecdi \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n th\u1eb3ng MN c\u0169ng thu\u1ed9c kh\u1ed1i \u0111a di\u1ec7n \u0111\u00f3. Ta g\u1ecdi \u0111\u00f3 l\u00e0 kh\u1ed1i \u0111a di\u1ec7n l\u1ed3i.<\/p>\n

\"\" \"\"<\/p>\n

 <\/p>\n

B\u00e0i 4 (trang 26 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho h\u00ecnh l\u0103ng tr\u1ee5 v\u00e0 h\u00ecnh ch\u00f3p c\u00f3 di\u1ec7n t\u00edch \u0111\u00e1y v\u00e0 chi\u1ec1u cao b\u1eb1ng nhau. T\u00ednh t\u1ec9 s\u1ed1 th\u1ec3 t\u00edch c\u1ee7a ch\u00fang.<\/strong><\/span><\/p>\n

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

G\u1ecdi S l\u00e0 di\u1ec7n t\u00edch \u0111\u00e1y v\u00e0 h l\u00e0 chi\u1ec1u cao c\u1ee7a h\u00ecnh l\u0103ng tr\u1ee5 v\u00e0 c\u1ee7a h\u00ecnh ch\u00f3p, ta c\u00f3:<\/p>\n

– Th\u1ec3 t\u00edch kh\u1ed1i l\u0103ng tr\u1ee5 l\u00e0: V1<\/sub>\u00a0= Sh<\/p>\n

– Th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p l\u00e0: V2<\/sub>= Sh\/3<\/p>\n

V\u1eady V1<\/sub>\/ V2<\/sub>=3Sh\/Sh = 3<\/p>\n

B\u00e0i 5 (trang 26 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho h\u00ecnh ch\u00f3p tam gi\u00e1c O.ABC c\u00f3 ba c\u1ea1nh OA, OB, OC \u0111\u00f4i m\u1ed9t vu\u00f4ng g\u00f3c v\u1edbi nhau v\u00e0 OA = a, OB = b, OC = c. H\u00e3y t\u00ednh \u0111\u01b0\u1eddng cao OH c\u1ee7a h\u00ecnh ch\u00f3p.<\/strong><\/span><\/p>\n

\"\" \"\" \"\"<\/p>\n

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

B\u00e0i 6 (trang 26 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u S.ABC c\u00f3 c\u1ea1nh AB b\u1eb1ng a. C\u00e1c c\u1ea1nh b\u00ean SA, SB, SC t\u1ea1o v\u1edbi \u0111\u00e1y m\u1ed9t g\u00f3c 60o<\/sup>. G\u1ecdi D l\u00e0 giao c\u1ee7a SA v\u1edbi m\u1eb7t ph\u1eb3ng qua BC v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi SA.<\/strong><\/span><\/p>\n

a)T\u00ednh t\u1ec9 s\u1ed1 th\u1ec3 t\u00edch gi\u1eefa hai kh\u1ed1i ch\u00f3p S.DBC v\u00e0 S.ABC.<\/strong><\/span><\/p>\n

b)T\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i ch\u00f3p S.DBC.<\/strong><\/span><\/p>\n

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

\"\" \"\"<\/p>\n

\"\"<\/p>\n

B\u00e0i 7 (trang 26 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho h\u00ecnh ch\u00f3p tam gi\u00e1c S.ABC c\u00f3 AB = 5a, BC = 6a, CA = 7a. C\u00e1c m\u1eb7t b\u00ean SAB, SBC, SCA t\u1ea1o v\u1edbi \u0111\u00e1y m\u1ed9t g\u00f3c 60o<\/sup>. T\u00ednh th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i ch\u00f3p \u0111\u00f3.<\/strong><\/span><\/p>\n

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

\"\" \"\"<\/p>\n

B\u00e0i 8 (trang 26 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y ABCD l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt, SA vu\u00f4ng g\u00f3c v\u1edbi \u0111\u00e1y v\u00e0 AB = a, AD=b, SA = c. L\u1ea5y c\u00e1c \u0111i\u1ec3m B\u2019, D\u2019 theo th\u1ee9 t\u1ef1 thu\u1ed9c SB, SD sao cho AB\u2019 vu\u00f4ng g\u00f3c v\u1edbi SB, AD\u2019 vu\u00f4ng g\u00f3c v\u1edbi SD. M\u1eb7t ph\u1eb3ng (AB\u2019D\u2019) c\u1eaft SC t\u1ea1i C\u2019. T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p S.AB\u2019C\u2019D\u2019.<\/strong><\/span><\/p>\n

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

\"\" \"\" \"\" \"\"<\/p>\n

B\u00e0i 9 (trang 26 SGK H\u00ecnh h\u1ecdc 12):\u00a0Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u S.ABCD . \u0110\u00e1y h\u00ecnh vu\u00f4ng c\u1ea1nh a, c\u1ea1nh b\u00ean t\u1ea1o v\u1edbi \u0111\u00e1y m\u1ed9t g\u00f3c 60o<\/sup>. G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m SC.M\u1eb7t ph\u1eb3ng \u0111i qua AM v\u00e0 song song v\u1edbi BD, c\u1eaft SB t\u1ea1i E v\u00e0 c\u1eaft SD t\u1ea1i F. T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p S.AEMF.<\/strong><\/span><\/p>\n

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

\"\"<\/p>\n

\"\" \"\"<\/p>\n

B\u00e0i 10 (trang 27 SGK H\u00ecnh h\u1ecdc 12):<\/strong><\/span><\/p>\n

Cho h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng tam gi\u00e1c ABC.A\u2019B\u2019C\u2019 c\u00f3 t\u1ea5t c\u1ea3 c\u00e1c c\u1ea1nh \u0111\u1ec1u b\u1eb1ng a.<\/strong><\/span><\/p>\n

a)T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i t\u1ee9 di\u1ec7n A\u2019BB\u2019C\u2019.<\/strong><\/span><\/p>\n

b)M\u1eb7t ph\u1eb3ng \u0111i qua A\u2019B\u2019 v\u00e0 tr\u1ecdng t\u00e2m tam gi\u00e1c ABC, c\u1eaft AC v\u00e0 BC l\u1ea7n l\u01b0\u1ee3t t\u1ea1i E v\u00e0 F. T\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p C.A\u2019B\u2019FE.<\/strong><\/span><\/p>\n

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

\"\"<\/p>\n

\"\"<\/p>\n

b)G\u1ecdi I, K l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB v\u00e0 A\u2019B\u2019, G l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c ABC.\u0110\u01b0\u1eddng th\u1eb3ng qua G, song song v\u1edbi AB c\u1eaft AC v\u00e0 BC l\u1ea7n l\u01b0\u1ee3t t\u1ea1i E v\u00e0 F, \u0111\u01b0\u1eddng th\u1eb3ng EF ch\u00ednh l\u00e0 giao tuy\u1ebfn c\u1ee7a hai m\u1eb7t ph\u1eb3ng (GA\u2019B\u2019) v\u00e0 (ABC).<\/p>\n

\"\" \"\"<\/p>\n

B\u00e0i 11 (trang 27 SGK H\u00ecnh h\u1ecdc 12):<\/strong><\/span><\/p>\n

Cho kh\u1ed1i h\u1ed9p ABCD.A\u2019B\u2019C\u2019D\u2019. G\u1ecdi E v\u00e0 F theo th\u1ee9 t\u1ef1 l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh BB\u2019 v\u00e0 DD\u2019. M\u1eb7t ph\u1eb3ng (CEF) chia kh\u1ed1i h\u1ed9p tr\u00ean l\u00e0m hai kh\u1ed1i \u0111a di\u1ec7n. T\u00ednh t\u1ec9 s\u1ed1 th\u1ec3 t\u00edch c\u1ee7a hai kh\u1ed1i \u0111a di\u1ec7n \u0111\u00f3.<\/strong><\/span><\/p>\n

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

\"\"<\/p>\n

G\u1ecdi O l\u00e0 t\u00e2m h\u00ecnh h\u1ed9p v\u00e0 t\u00e2m c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh BB\u2019D\u2019D. Khi \u0111\u00f3 O l\u00e0 trung \u0111i\u1ec3m c\u1ee7a EF.<\/p>\n

Ta c\u00f3: A\u2019 \u2208 CO (1)<\/p>\n

CO \u2282 mp(CEF)(2)<\/p>\n

M\u1eb7t kh\u00e1c A\u2019E \/\/ CF, A\u2019F \/\/ CE<\/p>\n

N\u00ean mp(CEF) c\u1eaft h\u00ecnh h\u1ed9p theo thi\u1ebft di\u1ec7n l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh A\u2019ECF.<\/p>\n

mp(CEF) chia h\u00ecnh h\u1ed9p ABCD.A\u2019B\u2019C\u2019D\u2019 th\u00e0nh hai kh\u1ed1i \u0111a di\u1ec7n (\u0110) v\u00e0 (\u0110\u2019).<\/p>\n

G\u1ecdi (\u0110) l\u00e0 kh\u1ed1i \u0111a di\u1ec7n c\u00f3 c\u00e1c \u0111\u1ec9nh l\u00e0 A, B, C, D, A\u2019, E, F v\u00e0 (\u0110\u2019) l\u00e0 kh\u1ed1i \u0111a di\u1ec7n c\u00f2n l\u1ea1i.<\/p>\n

Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua t\u00e2m O bi\u1ebfn c\u00e1c \u0111\u1ec9nh A, B, C, D, A\u2019, E, F c\u1ee7a \u0111a di\u1ec7n (\u0110) l\u1ea7n l\u01b0\u1ee3t th\u00e0nh c\u00e1c \u0111\u1ec9nh C\u2019, D\u2019, A\u2019, B\u2019, C, F, E c\u1ee7a kh\u1ed1i da di\u1ec7n (\u0110\u2019)<\/p>\n

Suy ra ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua t\u00e2m O bi\u1ebfn (\u0110) th\u00e0nh (\u0110\u2019), ngh\u0129a l\u00e0 hai h\u00ecnh \u0111a di\u1ec7n (\u0110) v\u00e0 (\u0110\u2019) b\u1eb1ng nhau.<\/p>\n

V\u1eady t\u1ec9 s\u1ed1 th\u1ec3 t\u00edch c\u1ee7a (\u0110) v\u00e0 (\u0110\u2019) b\u1eb1ng 1.<\/p>\n

B\u00e0i 12 (trang 27 SGK H\u00ecnh h\u1ecdc 12):<\/strong><\/span><\/p>\n

Cho h\u00ecnh l\u1eadp ph\u01b0\u01a1ng ABCD.A\u2019B\u2019C\u2019D\u2019 c\u1ea1nh a. G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m A\u2019B\u2019, N l\u00e0 trung \u0111i\u1ec3m BC.<\/strong><\/span><\/p>\n

a)T\u00ednh th\u1ec3 t\u00edch kh\u1ed1i t\u1ee9 di\u1ec7n ADMN<\/strong><\/span><\/p>\n

b)M\u1eb7t ph\u1eb3ng (DMN) chia kh\u1ed1i l\u1eadp ph\u01b0\u01a1ng \u0111\u00e3 cho th\u00e0nh hai kh\u1ed1i \u0111a di\u1ec7n. G\u1ecdi (H) l\u00e0 kh\u1ed1i \u0111a di\u1ec7n ch\u1ee9a \u0111\u1ec9nh A, (H\u2019) l\u00e0 kh\u1ed1i \u0111a di\u1ec7n c\u00f2n l\u1ea1i. T\u00ednh t\u1ec9 s\u1ed1 V(H)<\/sub>\/V(H’)<\/sub><\/strong><\/span><\/p>\n

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

\"\" \"\"<\/p>\n

\"\"<\/p>\n

b)-M\u1eb7t ph\u1eb3ng (DMN) c\u1eaft h\u00ecnh l\u1eadp ph\u01b0\u01a1ng theo thi\u1ebft di\u1ec7n MEDNF trong \u0111\u00f3 ME \/\/ ND, FN \/\/DE v\u00e0 chia h\u00ecnh l\u1eadp ph\u01b0\u01a1ng th\u00e0nh hai kh\u1ed1i \u0111a di\u1ec7n (H) v\u00e0 (H\u2019), g\u1ecdi ph\u1ea7n kh\u1ed1i l\u1eadp ph\u01b0\u01a1ng ch\u1ee9a A, B, A\u2019, m\u1eb7t ph\u1eb3ng (DMN) l\u00e0 (H)<\/p>\n

-Chia (H) th\u00e0nh c\u00e1c h\u00ecnh ch\u00f3p F.DBN, D.ABFMA\u2019 v\u00e0 D.A\u2019EM.<\/p>\n

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

B\u00e0i 1 (trang 26 SGK H\u00ecnh h\u1ecdc 12):\u00a0C\u00e1c \u0111\u1ec9nh, c\u1ea1nh, m\u1eb7t c\u1ee7a m\u1ed9t \u0111a di\u1ec7n ph\u1ea3i th\u1ecfa m\u00e3n nh\u1eefng t\u00ednh ch\u1ea5t n\u00e0o? L\u1eddi gi\u1ea3i: C\u00e1c \u0111\u1ec9nh, c\u1ea1nh, m\u1eb7t c\u1ee7a m\u1ed9t \u0111a di\u1ec7n ph\u1ea3i th\u1ecfa m\u00e3n nh\u1eefng t\u00ednh ch\u1ea5t: – M\u1ed7i \u0111\u1ec9nh l\u00e0 \u0111\u1ec9nh chung c\u1ee7a \u00edt nh\u1ea5t ba c\u1ea1nh, ba m\u1eb7t; – M\u1ed7i c\u1ea1nh l\u00e0 […]<\/p>\n","protected":false},"author":3,"featured_media":20665,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1298],"tags":[1356,1355],"yoast_head":"\nH\u00ecnh H\u1ecdc - Ch\u01b0\u01a1ng I: Kh\u1ed1i \u0111a di\u1ec7n - \u00d4n t\u1eadp<\/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-khoi-da-dien-tap\/\" \/>\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: Kh\u1ed1i \u0111a di\u1ec7n - \u00d4n t\u1eadp\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 1 (trang 26 SGK H\u00ecnh h\u1ecdc 12):\u00a0C\u00e1c \u0111\u1ec9nh, c\u1ea1nh, m\u1eb7t c\u1ee7a m\u1ed9t \u0111a di\u1ec7n ph\u1ea3i th\u1ecfa m\u00e3n nh\u1eefng t\u00ednh ch\u1ea5t n\u00e0o? 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