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{"id":29422,"date":"2018-05-03T23:39:15","date_gmt":"2018-05-03T16:39:15","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=29422"},"modified":"2018-05-13T10:33:09","modified_gmt":"2018-05-13T03:33:09","slug":"hinh-hoc-bai-4-hai-ma%cc%a3t-pha%cc%89ng-song-song","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/hinh-hoc-bai-4-hai-ma%cc%a3t-pha%cc%89ng-song-song\/","title":{"rendered":"H\u00ecnh h\u1ecdc – Ch\u01b0\u01a1ng 3 – B\u00e0i 4 : Hai m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c"},"content":{"rendered":"

B\u00e0i 1 (trang 113 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho ba m\u1eb7t ph\u1eb3ng (\u03b1), (\u03b2), (\u03b3), nh\u1eefng m\u1ec7nh \u0111\u1ec1 n\u00e0o sau \u0111\u00e2y \u0111\u00fang?<\/p>\n

a) N\u1ebfu (\u03b1) \u22a5 (\u03b2) v\u00e0 (\u03b1) \/\/ (\u03b3) th\u00ec (\u03b2) \u22a5 (\u03b3).<\/p>\n

b) N\u1ebfu (\u03b1) \u22a5 (\u03b2) v\u00e0 (\u03b1) \u22a5 (\u03b3) th\u00ec (\u03b2) \/\/ (\u03b3).<\/p>\n

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

a) \u0110\u00fang, v\u00ec n\u1ebfu g\u1ecdi m l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi \u03b2 v\u00e0 n l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi hai m\u1eb7t ph\u1eb3ng song song \u03b1, \u03b3 th\u00ec g\u00f3c (m, n) = (\u03b2, \u03b1) = (\u03b2, \u03b3), m\u00e0 \u03b2 \u22a5 \u03b1 n\u00ean \u03b2 \u22a5 \u03b3.<\/p>\n

b) Sai, v\u00ec hai m\u1eb7t ph\u1eb3ng (\u03b2), (\u03b3) c\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi mp(\u03b1) c\u00f3 th\u1ec3 song song ho\u1eb7c c\u1eaft nhau.<\/p>\n

B\u00e0i 2 (trang 113 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho hai m\u1eb7t ph\u1eb3ng (\u03b1), (\u03b2) vu\u00f4ng g\u00f3c v\u1edbi nhau. Ng\u01b0\u1eddi ta l\u1ea5y tr\u00ean giao tuy\u1ebfn \u0394 c\u1ee7a hai m\u1eb7t ph\u1eb3ng \u0111\u00f3 hai \u0111i\u1ec3m A v\u00e0 B sao cho AB = 8cm. G\u1ecdi C l\u00e0 m\u1ed9t \u0111i\u1ec3m tr\u00ean (\u03b1) v\u00e0 D l\u00e0 m\u1ed9t \u0111i\u1ec3m tr\u00ean (\u03b2) sao cho AC v\u00e0 BD c\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi giao tuy\u1ebfn \u0394 v\u00e0 AC = 6cm, BD = 24cm. T\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n CD.<\/p>\n

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

\"\"<\/p>\n

\"\"<\/p>\n

B\u00e0i 3 (trang 113 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Trong m\u1eb7t ph\u1eb3ng (\u03b1) cho tam gi\u00e1c ABC vu\u00f4ng \u1edf B. M\u1ed9t \u0111o\u1ea1n th\u1eb3ng AD vu\u00f4ng g\u00f3c v\u1edbi (\u03b1) t\u1ea1i A. Ch\u1ee9ng minh r\u1eb1ng:<\/p>\n

a) (ABD) l\u00e0 g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng (ABC) v\u00e0 (DBC)<\/p>\n

b) HK \/\/ BC v\u1edbi H v\u00e0 K l\u1ea7n l\u01b0\u1ee3t l\u00e0 giao \u0111i\u1ec3m c\u1ee7a DB v\u00e0 DC v\u1edbi mp(P) \u0111i qua A v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi DB.<\/p>\n

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

\"\"<\/p>\n

\"\"<\/p>\n

B\u00e0i 4 (trang 114 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho hai m\u1eb7t ph\u1eb3ng (\u03b1), (\u03b2) c\u1eaft nhau v\u00e0 m\u1ed9t \u0111i\u1ec3m M kh\u00f4ng thu\u1ed9c (\u03b1) v\u00e0 (\u03b2). Ch\u1ee9ng minh r\u1eb1ng qua \u0111i\u1ec3m M c\u00f3 m\u1ed9t v\u00e0 ch\u1ec9 m\u1ed9t m\u1eb7t ph\u1eb3ng (P) vu\u00f4ng g\u00f3c v\u1edbi (\u03b1) v\u00e0 (\u03b2). N\u1ebfu (\u03b1) \/\/ (\u03b2) th\u00ec k\u1ebft qu\u1ea3 tr\u00ean s\u1ebd thay \u0111\u1ed5i nh\u01b0 th\u1ebf n\u00e0o?<\/p>\n

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

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

V\u1eady (MHK) ch\u00ednh l\u00e0 m\u1eb7t ph\u1eb3ng \u0111i qua M v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi (\u03b1) v\u00e0 (\u03b2).<\/p>\n

K\u1ebft qu\u1ea3: M\u1eb7t ph\u1eb3ng (P) c\u1ea7n d\u1ef1ng (t\u1ee9c mp(MHK)) l\u00e0 m\u1eb7t ph\u1eb3ng \u0111i qua M v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi \u0394.<\/p>\n

V\u00ec qua m\u1ed9t \u0111i\u1ec3m ch\u1ec9 c\u00f3 duy nh\u1ea5t m\u1ed9t m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng cho tr\u01b0\u1edbc n\u00ean (P) l\u00e0 duy nh\u1ea5t.<\/p>\n

N\u1ebfu (\u03b1) \/\/ (\u03b2) th\u00ec qua M ta ch\u1ec9 c\u00f3 th\u1ec3 v\u1ebd m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng \u0394 vu\u00f4ng g\u00f3c v\u1edbi (\u03b1) v\u00e0 (\u03b2). B\u1ea5t k\u00ec m\u1eb7t ph\u1eb3ng (P) n\u00e0o ch\u1ee9a \u0394 c\u0169ng \u0111\u1ec1u vu\u00f4ng g\u00f3c v\u1edbi (\u03b1), (\u03b2). Tr\u01b0\u1eddng h\u1ee3p n\u00e0y, qua M c\u00f3 v\u00f4 s\u1ed1 m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c v\u1edbi (\u03b1), (\u03b2).<\/p>\n

B\u00e0i 5 (trang 114 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh l\u1eadp ph\u01b0\u01a1ng ABCD.A’B’C’D’. Ch\u1ee9ng minh r\u1eb1ng:<\/p>\n

a) M\u1eb7t ph\u1eb3ng (AB’C’D) vu\u00f4ng g\u00f3c v\u1edbi (BCD’A’)<\/p>\n

b) \u0110\u01b0\u1eddng th\u1eb3ng AC’ vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (A’BD)<\/p>\n

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

\"\"<\/p>\n

\"\"<\/p>\n

B\u00e0i 6 (trang 114 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 thoi c\u1ea1nh a v\u00e0 c\u00f3 SA = SB = SC = a. Ch\u1ee9ng minh r\u1eb1ng:<\/p>\n

a) M\u1eb7t ph\u1eb3ng (ABCD) vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (SBD).<\/p>\n

b) Tam gi\u00e1c SBD l\u00e0 tam gi\u00e1c vu\u00f4ng.<\/p>\n

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

\"\"<\/p>\n

\"\"<\/p>\n

B\u00e0i 7 (trang 114 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt ABCD.A’B’C’D’. C\u00f3 AB = a, BC= b, CC’= c.<\/p>\n

a) Ch\u1ee9ng minh r\u1eb1ng m\u1eb7t ph\u1eb3ng (ADC’B’) vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (ABB’A’).<\/p>\n

b) T\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o AC’ theo a, b v\u00e0 c.<\/p>\n

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

\"\"<\/p>\n

\"\"<\/p>\n

B\u00e0i 8 (trang 114 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0T\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a m\u1ed9t h\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u1ea1nh a.<\/p>\n

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

\"\"<\/p>\n

B\u00e0i 8 (trang 114 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0T\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a m\u1ed9t h\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u1ea1nh a.<\/p>\n

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

\"\"<\/p>\n

H\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u S.ABC c\u00f3 \u0111\u00e1y l\u00e0 tam gi\u00e1c \u0111\u1ec1u ABC v\u00e0 ch\u00e2n \u0111\u01b0\u1eddng cao tr\u00f9ng v\u1edbi t\u00e2m c\u1ee7a \u0111\u00e1y. H l\u00e0 t\u00e2m c\u1ee7a tam gi\u00e1c \u0111\u1ec1u ABC<\/p>\n

Ta c\u00f3: AH \u22a5 BC<\/p>\n

M\u00e0 AH l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a SA tr\u00ean (ABC)<\/p>\n

\u21d2 BC \u22a5SA.<\/p>\n

T\u01b0\u01a1ng t\u1ef1 AC \u22a5 BH.<\/p>\n

BH l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a SB tr\u00ean (ABC)<\/p>\n

\u21d2 AC \u22a5 SB.<\/p>\n

B\u00e0i 10 (trang 114 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u S.ABCD c\u00f3 c\u00e1c c\u1ea1nh b\u00ean v\u00e0 c\u00e1c c\u1ea1nh \u0111\u00e1y \u0111\u1ec1u b\u1eb1ng a. G\u1ecdi O l\u00e0 t\u00e2m c\u1ee7a h\u00ecnh vu\u00f4ng ABCD.<\/p>\n

a) T\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n SO.<\/p>\n

b) G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n SC. Ch\u1ee9ng minh hai m\u1eb7t ph\u1eb3ng (MBD) v\u00e0 (SAC) vu\u00f4ng g\u00f3c v\u1edbi nhau.<\/p>\n

c) T\u00ednh \u0111\u1ed9 d\u00e0i \u0111o\u1ea1n OM v\u00e0 t\u00ednh g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng (MBD) v\u00e0 (ABCD).<\/p>\n

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

\"\"<\/p>\n

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

B\u00e0i 11 (trang 114 SGK H\u00ecnh h\u1ecdc 11):<\/b><\/p>\n

\"\"<\/p>\n

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

 <\/p>\n

\"\"<\/p>\n

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

 <\/p>\n

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

B\u00e0i 1 (trang 113 SGK H\u00ecnh h\u1ecdc 11):\u00a0Cho ba m\u1eb7t ph\u1eb3ng (\u03b1), (\u03b2), (\u03b3), nh\u1eefng m\u1ec7nh \u0111\u1ec1 n\u00e0o sau \u0111\u00e2y \u0111\u00fang? a) N\u1ebfu (\u03b1) \u22a5 (\u03b2) v\u00e0 (\u03b1) \/\/ (\u03b3) th\u00ec (\u03b2) \u22a5 (\u03b3). b) N\u1ebfu (\u03b1) \u22a5 (\u03b2) v\u00e0 (\u03b1) \u22a5 (\u03b3) th\u00ec (\u03b2) \/\/ (\u03b3). L\u1eddi gi\u1ea3i: a) \u0110\u00fang, v\u00ec n\u1ebfu g\u1ecdi m […]<\/p>\n","protected":false},"author":3,"featured_media":29423,"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 3 - B\u00e0i 4 : Hai m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c<\/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-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 3 - B\u00e0i 4 : Hai m\u1eb7t ph\u1eb3ng vu\u00f4ng g\u00f3c\" \/>\n<meta property=\"og:description\" content=\"B\u00e0i 1 (trang 113 SGK H\u00ecnh h\u1ecdc 11):\u00a0Cho ba m\u1eb7t ph\u1eb3ng (\u03b1), (\u03b2), (\u03b3), nh\u1eefng m\u1ec7nh \u0111\u1ec1 n\u00e0o sau \u0111\u00e2y \u0111\u00fang? a) N\u1ebfu (\u03b1) \u22a5 (\u03b2) v\u00e0 (\u03b1) \/\/ (\u03b3) th\u00ec (\u03b2) \u22a5 (\u03b3). b) N\u1ebfu (\u03b1) \u22a5 (\u03b2) v\u00e0 (\u03b1) \u22a5 (\u03b3) th\u00ec (\u03b2) \/\/ (\u03b3). 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