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{"id":22451,"date":"2018-03-19T17:58:05","date_gmt":"2018-03-19T10:58:05","guid":{"rendered":"https:\/\/lop12.edu.vn\/?p=22451"},"modified":"2018-03-19T17:58:05","modified_gmt":"2018-03-19T10:58:05","slug":"hinh-hoc-chuong-1-bai-3-phep-vi-tu-va-su-dong-dang-cua-cac-khoi-da-dien-cac-khoi-da-dien-deu","status":"publish","type":"post","link":"https:\/\/lop12.edu.vn\/hinh-hoc-chuong-1-bai-3-phep-vi-tu-va-su-dong-dang-cua-cac-khoi-da-dien-cac-khoi-da-dien-deu\/","title":{"rendered":"H\u00ecnh h\u1ecdc – Ch\u01b0\u01a1ng 1 – B\u00e0i 3: Ph\u00e9p vi t\u1ef1 v\u00e0 s\u1ef1 \u0111\u1ed3ng d\u1ea1ng c\u1ee7a c\u00e1c kh\u1ed1i \u0111a di\u1ec7n. C\u00e1c kh\u1ed1i \u0111a di\u1ec7n \u0111\u1ec1u"},"content":{"rendered":"

B\u00e0i 11 (trang 20 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n

Ch\u1ee9ng minh r\u1eb1ng ph\u00e9p v\u1ecb t\u1ef1 bi\u1ebfn m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng a th\u00e0nh \u0111\u01b0\u1eddng th\u1eb3ng a\u2019 song song a th\u00e0nh \u0111\u01b0\u1eddng th\u1eb3ng a\u2019. h\u01a1n n\u1eefa (\u03b1) th\u00e0nh m\u1ed9t m\u1eb7t ph\u1eb3ng (\u03b1’) song song ho\u1eb7c tr\u00f9ng v\u1edbi \u03b1.<\/p>\n

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

– Do ph\u00e9p v\u1ecb t\u1ef1 bi\u1ebfn ba \u0111i\u1ec3m th\u1eb1ng h\u00e0nh th\u00e0nh 3 \u0111i\u1ec3m th\u1eb1ng h\u00e0ng n\u00ean n\u00f3 bi\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng a th\u00e0nh a\u2019. H\u01a1n n\u1eefa a\u2019 song song ho\u1eb7c tr\u00f9ng v\u1edbi a<\/p>\n

Th\u1eadt v\u1eady, tr\u00ean a l\u1ea5y \u0111i\u1ec3m A, B; Gi\u1ea3 s\u1eed V0,k<\/sub>\u00a0bi\u1ebfn A th\u00e0nh A\u2019 bi\u1ebfn B th\u00e0nh B\u2019.<\/p>\n

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

\"\"<\/p>\n

– Tr\u01b0\u1eddng h\u1ee3p 1: K = 1 ho\u1eb7c O \u2208 a th\u00ec A\u2019B\u2019 = AB hay a = a\u2019.<\/p>\n

– Tr\u01b0\u1eddng h\u1ee3p 2: k \u2260 1 v\u00e0 O \u2208a th\u00ec A\u2019B\u2019 \/\/ AB hay a\u2019 \/\/ a<\/p>\n

Ph\u00e9p v\u1ecb t\u1ef1 V0,k<\/sub>\u00a0bi\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng th\u00e0nh \u0111\u01b0\u1eddng th\u1eb3ng song song ho\u1eb7c tr\u00f9ng v\u1edbi n\u00f3 n\u00ean bi\u1ebfn hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau th\u00e0nh hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau. V\u1eady n\u00f3 bi\u1ebfn mp(\u03b1) th\u00e0nh m\u1eb7t ph\u1eb3ng (\u03b10′). H\u01a1n n\u1eefa mp(\u03b1’) song song ho\u1eb7c trung v\u1edbi mp(\u03b1). Th\u1eadt v\u1eady:<\/p>\n

– N\u1ebfu O \u2208 (\u03b1) th\u00ec V0,k<\/sub>\u00a0bi\u1ebfn A \u2208(\u03b1) th\u00e0nh A\u2019 sao cho\u00a0OA’\u2192<\/i>=kOA\u2192<\/i>.<\/p>\n

=> A’\u2208OA hay A’\u2208mp(\u03b1) suy ra mp(\u03b1’)=mp(\u03b1).<\/p>\n

– N\u1ebfu k=1 th\u00ec V0,k<\/sub>) bi\u1ebfn A \u2208mp(\u03b1) th\u00e0nh A\u2019 = A n\u1ebfn mp(\u03b1’)=mp(\u03b1).<\/p>\n

– N\u1ebfu O \u2208 mp(\u03b1) v\u00e0 k \u2260 1. Tr\u00ean mp(\u03b1) l\u1ea5y hai \u0111\u01b0\u1eddng th\u1eb3ng a, b c\u1eaft a\u2019, b t\u1ea1i A\u2019 ( V0,k<\/sub>\u00a0bi\u1ebfn A th\u00e0nh A\u2019) v\u00e0 a\u2019 \/\/ a, b\u2019 \/\/ a. N\u00ean mp(\u03b1) ch\u1ee9a a\u2019, b\u2019 song song v\u1edbi mp(\u03b1) ch\u1ee9a (a, b).<\/p>\n

\"\"<\/p>\n

B\u00e0i 12 (trang 20 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n

Cho m\u1ed9t kh\u1ed1i t\u1ee9 di\u1ec7n \u0111\u1ec1u, h\u00e3y ch\u1ee9ng minh r\u1eb1ng.<\/p>\n

a) C\u00e1c tr\u1ecdng t\u00e2m c\u1ee7a c\u00e1c m\u1eb7t c\u1ee7a n\u00f3 l\u00e0 c\u00e1c \u0111\u1ec9nh c\u1ee7a m\u1ed9t kh\u1ed1i t\u1ee9 di\u1ec7n \u0111\u1ec1u.<\/p>\n

b) C\u00e1c trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh c\u1ee7a n\u00f3 l\u00e0 c\u00e1c \u0111\u1ec9nh c\u1ee7a m\u1ed9t kh\u1ed1i t\u00e2m m\u1eb7t \u0111\u1ec1u<\/p>\n

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

<\/div>\n

\"\"<\/p>\n

a) G\u1ecdi G l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a t\u1ee9 di\u1ec7n ABCD. A\u2019, B\u2019, C\u2019, D\u2019 l\u1ea7n l\u01b0\u1ee3t l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a c\u00e1c m\u1eb7t \u0111\u1ed1i di\u1ec7n v\u1edbi c\u00e1c \u0111\u1ec9nh A, B, C, D. Theo t\u00ednh ch\u1ea5t c\u1ee7a tr\u1ecdng t\u00e2m t\u1ee9 di\u1ec7n \u0111\u1ec1u, ta c\u00f3:<\/p>\n

\"\"<\/p>\n

N\u00ean VG,1\/3<\/sub>\u00a0bi\u1ebfn A, B, C, D l\u1ea7n l\u01b0\u1ee3t th\u00e0nh A\u2019, B\u2019, C\u2019, D\u2019<\/p>\n

hay VG,-1\/3<\/sub>\u00a0bi\u1ebfn t\u1ee9 di\u1ec7n ABCD th\u00e0nh t\u1ee9 di\u1ec7n A\u2019B\u2019C\u2019D\u2019 n\u00ean A\u2019B\u2019C\u2019D\u2019 l\u00e0 t\u1ee9 di\u1ec7n d\u1ec1u.<\/p>\n

\"\"<\/p>\n

b) X\u00e9t t\u1ee9 di\u1ec7n \u0111\u1ec1u ABCD. G\u1ecdi M,N, P, Q, E, F l\u1ea7n l\u01b0\u1ee3t l\u00e0n trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh Ab, BC, CD, DA, AC, BD.<\/p>\n

D\u1ec5 th\u1ea5y E c\u00f9ng v\u1edbi 4 \u0111i\u1ec3m M, N, P, Q l\u00e0 c\u00e1c \u0111\u1ec9nh c\u1ee7a kh\u1ed1i ch\u00f3p t\u1ee9 gi\u00e1c E.MNPQ c\u00f3 4 m\u1eb7t b\u00ean l\u00e0 tam gi\u00e1c \u0111\u1ec1u. Ta c\u0169ng c\u00f3 F.MNPQ l\u00e0 kh\u1ed1i ch\u00f3p tam gi\u00e1c \u0111\u1ec1u.<\/p>\n

V\u1eady M, N, P, Q, E, F l\u00e0 c\u00e1c \u0111\u1ec9nh c\u1ee7a m\u1ed9t kh\u1ed1i 8 m\u1eb7t \u0111\u1ec1u.<\/p>\n

B\u00e0i 13 (trang 20 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b><\/p>\n

Hai \u0111\u1ec9nh c\u1ee7a m\u1ed9t kh\u1ed1i tam m\u1eb7t \u0111\u1ec1u cho tr\u01b0\u1edbc g\u1ecdi l\u00e0 c\u00e1c \u0111\u1ec9nh kh\u1ed1i di\u1ec7n n\u1ebfu chung kh\u00f4ng thu\u1ed9c c\u00f9ng m\u1ed9t c\u1ea1nh c\u1ee7a kh\u1ed1i di\u1ec7n \u0111\u00f3. \u0110o\u1ea1n th\u1eb3ng n\u1ed1i hai \u0111\u1ec9nh \u0111\u1ed1i di\u1ec7n g\u1ecdi l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a kh\u1ed1i tam gi\u00e1c \u0111\u1ec1u. ch\u1ee9ng minh r\u1eb1ng trong kh\u1ed1i t\u1eafm m\u1eb7t \u0111\u1ec1u:<\/p>\n

a) Ba \u0111\u01b0\u1eddng ch\u00e9o c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng.<\/p>\n

b) Ba \u0111\u01b0\u1eddng ch\u00e9p \u0111\u00f4i m\u1ed9t vu\u00f4ng g\u00f3c.<\/p>\n

c) Ba \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng nhau.<\/p>\n

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

<\/div>\n

\"\"<\/p>\n

X\u00e9t kh\u1ed1i 8 m\u1eb7t \u0111\u1ec1u ABCDEF. V\u00ec A, B, C, D c\u00e1ch \u0111\u1ec1u E v\u00e0 F n\u00ean A, B, A, D c\u00f9ng thu\u1ed9c m\u1eb7t ph\u1eb3ng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n EF v\u00e0 do \u0111\u00f3 ABCD l\u00e0 h\u00ecnh thoi ( v\u00ec AB = BC = CD = DA)<\/p>\n

a) T\u1ee9 gi\u00e1c ABCD l\u00e0 h\u00ecnh thoi n\u00ean AC v\u00e0 BD c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m O c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng.<\/p>\n

T\u01b0\u01a1ng t\u1ef1, AC v\u00e0 EF c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng.<\/p>\n

V\u1eady AC, BD, EF c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng.<\/p>\n

b) T\u1ee9 gi\u00e1c ABCD l\u00e0 h\u00ecnh thoi n\u00ean ta c\u0169ng c\u00f3 AC \u22a5 BD, t\u01b0\u01a1ng t\u1ef1 AC \u22a5 EF,BD \u22a5 EF, v\u1eady AC, BD, EF \u0111\u00f4i m\u1ed9t vu\u00f4ng g\u00f3c.<\/p>\n

c) C\u00e1ch 1. D\u1ec5 th\u1ea5y \u0394ABD=\u0394EBD (c-c-c) nen c\u00e1c trung tuy\u1ebfn t\u01b0\u01a1ng \u1ee9ng b\u1eb1ng nhau t\u1ee9 l\u00e0 AO = EO<\/p>\n

=> AC = EF, t\u01b0\u01a1ng t\u1ef1, AC = BD.<\/p>\n

V\u1eady AC = BD = EF (\u0111pcm).<\/p>\n

C\u00e1ch 2. V\u00ec EO \u22a5 (ABCD) n\u00ean AO, OB l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a EA, EB tr\u00ean (ABCD) m\u00e0 EA = EB => OA = OB => AC = DB. T\u01b0\u01a1ng t\u1ef1, AC = EF.<\/p>\n

V\u1eady AC = BD = EF.<\/p>\n

B\u00e0i 14 (trang 20 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao):<\/b>\u00a0Ch\u1ee9ng minh r\u1eb1ng:<\/p>\n

a) T\u00e2m c\u00e1c m\u1eb7t c\u1ee7a kh\u1ed1i l\u1eadp Ph\u01b0\u01a1ng cho tr\u01b0\u1edbc l\u00e0 c\u00e1c \u0111\u1ec9nh c\u1ee7a m\u1ed9t kh\u1ed1i t\u00e1m m\u1eb7t \u0111\u1ec1u.<\/p>\n

b) T\u00e1m c\u00e1c m\u1eb7t c\u1ee7a m\u1ed9t kh\u1ed1i t\u00e1m m\u1eb7t \u0111\u1ec1u cho tr\u01b0\u1edbc l\u00e0 c\u00e1c \u0111\u1ec9nh c\u1ee7a kh\u1ed1i l\u1eadp Ph\u01b0\u01a1ng.<\/p>\n

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

<\/div>\n

\"\"<\/p>\n

a) X\u00e9t kh\u1ed1i l\u1eadp Ph\u01b0\u01a1ng ABCD.A\u2019B\u2019C\u2019D\u2019 c\u1ea1nh a. g\u1ecdi O1<\/sub>, O2<\/sub>,O3<\/sub>,O4<\/sub>,O5<\/sub>,O6<\/sub>\u00a0l\u1ea7n l\u01b0\u1ee3t l\u00e0 t\u00e2m c\u1ee7a c\u00e1c m\u1eb7t ph\u1eb3ng ABCD, A\u2019B\u2019C\u2019D\u2019, ABB\u2019A\u2019, BCC\u2019B\u2019, C\u0110\u2019C\u2019, DAA\u2019D.<\/p>\n

Ta c\u00f3: O1<\/sub>\u00a0l\u00e0 trung \u0111i\u1ec3m c\u1ee7a BD, O3<\/sub>\u00a0l\u00e0 trung \u0111i\u1ec3m c\u1ee7a A\u2019B\u2019 n\u00ean:<\/p>\n

\"\"<\/p>\n

T\u01b0\u01a1ng t\u1ef1: O1<\/sub>\u00a0O4<\/sub>=O1<\/sub>\u00a0O5<\/sub>=O1<\/sub>\u00a0O6<\/sub>=O3<\/sub>\u00a0O4<\/sub>=O4<\/sub>\u00a0O5<\/sub>=O5<\/sub>\u00a0O6<\/sub>=O1<\/sub>\u00a0O6<\/sub>=O3<\/sub>O4<\/sub>=O4<\/sub>\u00a0O5<\/sub>=O5<\/sub>\u00a0O6<\/sub>=O6<\/sub>\u00a0O3<\/sub>=O2<\/sub>\u00a0O3<\/sub>=O2<\/sub>\u00a0O4<\/sub>=O2<\/sub>\u00a0O5<\/sub>=O2<\/sub>\u00a0O6<\/sub>=(a\u221a2)\/2<\/p>\n

V\u1eady O1<\/sub>,O2<\/sub>,O3<\/sub>,O4<\/sub>,O_5,O_6 l\u1ea7n l\u01b0\u1ee3t l\u00e0 c\u00e1c \u0111\u1ec9nh c\u1ee7a m\u1ed9t kh\u1ed1i l\u1eadp Ph\u01b0\u01a1ng.<\/p>\n

\"\"<\/p>\n

b) X\u00e9t kh\u1ed1i 8 m\u1eb7t \u0111\u1ec1u ABCDEF. G\u1ecdi O1<\/sub>, O2<\/sub>,O3<\/sub>,O4<\/sub>,O5<\/sub>,O6<\/sub>, O7<\/sub>, O8<\/sub>\u00a0l\u1ea7n l\u01b0\u1ee3t l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a c\u00e1c m\u1eb7t EAB, EBC, ECD, EDA, FAB, FBC, FCD, FDA.<\/p>\n

– G\u1ecdi M, N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB, BC.<\/p>\n

ta c\u00f3: O1<\/sub>,O2<\/sub>\u00a0l\u00e0 tr\u1ecdng t\u00e2m \u0394EAB, EBC n\u00ean:<\/p>\n

\"\"<\/p>\n

=> O1<\/sub>\u00a0O2<\/sub>\u00a0\/\/ MN<\/p>\n

\"\"<\/p>\n

=> O1<\/sub>\u00a0O2<\/sub>\u00a0\/\/ O3<\/sub>\u00a0O4<\/sub>\u00a0v\u00e0 O1<\/sub>\u00a0O2<\/sub>\u00a0\/\/ O_3 O4<\/sub><\/p>\n

=> T\u1ee9 gi\u00e1c O1<\/sub>\u00a0O2<\/sub>\u00a03<\/sub>\u00a0O4<\/sub>\u00a0l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh.<\/p>\n

L\u1ea1i c\u00f3: O1<\/sub>\u00a0O4<\/sub>\u00a0\/\/ BD, O1<\/sub>\u00a0O4<\/sub>=BD\/3 k\u1ebft h\u1ee3p (*) v\u00e0 l\u01b0u \u00fd r\u1eb1ng.<\/p>\n

AC = DB, AC \u22a5 BD => O1<\/sub>\u00a0O2<\/sub>=O1<\/sub>\u00a0O_4, O1<\/sub>\u00a0O3<\/sub>\u00a0\u22a5 O1<\/sub>\u00a0O4<\/sub>\u00a0n\u00ean t\u1ee9 gi\u00e1c O1<\/sub>\u00a0O2<\/sub>\u00a0O3<\/sub>\u00a0O4<\/sub>\u00a0l\u00e0 h\u00ecnh vu\u00f4ng.<\/p>\n

– Ho\u00e0n to\u00e0n t\u01b0\u01a1ng \u1ee9ng ta c\u00f3: O1<\/sub>\u00a0O2<\/sub>\u00a0O6<\/sub>\u00a0O5<\/sub>,O2<\/sub>\u00a0O3<\/sub>\u00a0O7<\/sub>\u00a0O6<\/sub>,O3<\/sub>\u00a0O4<\/sub>,O8<\/sub>\u00a0O7<\/sub>,O4<\/sub>\u00a0O1<\/sub>\u00a0O5<\/sub>\u00a0O8<\/sub>,O5<\/sub>\u00a0O6<\/sub>\u00a0O7<\/sub>\u00a0O8<\/sub>\u00a0l\u00e0 c\u00e1c h\u00ecnh vu\u00f4ng.<\/p>\n

V\u1eady O1<\/sub>, O2<\/sub>,O3<\/sub>,O4<\/sub>,O5<\/sub>,O6<\/sub>, O7<\/sub>, O8<\/sub>\u00a0l\u00e0 c\u00e1c \u0111\u1ec9nh c\u1ee7a m\u1ed9t kh\u1ed1i l\u1eadp Ph\u01b0\u01a1ng.<\/p>\n

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

B\u00e0i 11 (trang 20 sgk H\u00ecnh H\u1ecdc 12 n\u00e2ng cao): Ch\u1ee9ng minh r\u1eb1ng ph\u00e9p v\u1ecb t\u1ef1 bi\u1ebfn m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng a th\u00e0nh \u0111\u01b0\u1eddng th\u1eb3ng a\u2019 song song a th\u00e0nh \u0111\u01b0\u1eddng th\u1eb3ng a\u2019. h\u01a1n n\u1eefa (\u03b1) th\u00e0nh m\u1ed9t m\u1eb7t ph\u1eb3ng (\u03b1’) song song ho\u1eb7c tr\u00f9ng v\u1edbi \u03b1. L\u1eddi gi\u1ea3i: – Do ph\u00e9p v\u1ecb t\u1ef1 bi\u1ebfn ba […]<\/p>\n","protected":false},"author":3,"featured_media":22452,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[1302],"tags":[1392,1393],"yoast_head":"\nH\u00ecnh h\u1ecdc - Ch\u01b0\u01a1ng 1 - B\u00e0i 3: Ph\u00e9p vi t\u1ef1 v\u00e0 s\u1ef1 \u0111\u1ed3ng d\u1ea1ng c\u1ee7a c\u00e1c kh\u1ed1i \u0111a di\u1ec7n. 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