B\u00e0i 1 (trang 125 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, cho c\u00e1c \u0111i\u1ec3m A (1;1), B(0;3), C(2;4) .X\u00e1c \u0111\u1ecbnh \u1ea3nh c\u1ee7a tam gi\u00e1c ABC qua c\u00e1c ph\u00e9p bi\u1ebfn h\u00ecnh sau.<\/p>\n

(a)Ph\u00e9p t\u1ecbnh ti\u1ebfn theo vector v = (2;1).<\/p>\n

(b)Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua tr\u1ee5c Ox<\/p>\n

(c)Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua t\u00e2m I(2;1).<\/p>\n

(d)Ph\u00e9p quay t\u00e2m O g\u00f3c 90^{o<\/sup>.<\/p>\n}

(e)Ph\u00e9p \u0111\u1ed3ng d\u1ea1ng c\u00f3 \u0111\u01b0\u1ee3c b\u1eb1ng c\u00e1ch th\u1ef1c hi\u1ec7n li\u00ean ti\u1ebfp ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua tr\u1ee5 Oy v\u00e0 ph\u00e9p v\u1ecb t\u1ef1 t\u00e2m O t\u1ec9 s\u1ed1 k = -2<\/p>\n

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

G\u1ecdi tam gi\u00e1c A^{‘<\/sup>B‘<\/sup>C‘<\/sup>\u00a0l\u00e0 \u1ea3nh c\u1ee7a tam gi\u00e1c ABC qua ph\u00e9p bi\u1ebfn h\u00ecnh tr\u00ean.<\/p>\n}

<\/p>\n

B\u00e0i 2 (trang 125 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho tam gi\u00e1c ABC n\u1ed9i ti\u1ebfp \u0111\u01b0\u1eddng tr\u00f2n t\u00e2m O. G\u1ecdi G v\u00e0 H t\u01b0\u01a1ng \u1ee9ng l\u00e0 tr\u1ecdng t\u00e2m v\u00e0 tr\u1ef1c t\u00e2m c\u1ee7a tam gi\u00e1c, c\u00e1c \u0111i\u1ec3m A^{‘<\/sup>, B‘<\/sup>,C‘<\/sup>\u00a0l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh BC, CA, AB.<\/p>\n}

(a) T\u00ecm ph\u00e9p v\u1ecb t\u1ef1 F bi\u1ebfn A, B, C t\u01b0\u01a1ng t\u1ee9ng th\u00e0nh A^{‘<\/sup>, B‘<\/sup>,C‘<\/sup><\/p>\n}

(b) Ch\u1ee9ng minh r\u1eb1ng O, G, H th\u1eb3ng h\u00e0ng.<\/p>\n

(c) T\u00ecm \u1ea3nh c\u1ee7a O qua ph\u00e9p v\u1ecb t\u1ef1 F<\/p>\n

(d) G\u1ecdi A^{”<\/sup>, B”<\/sup>,C”<\/sup>\u00a0l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c \u0111o\u1ea1n th\u1eb3ng AH, BH, CH; A_{1<\/sub>, B1<\/sub>,C1<\/sub>\u00a0theo th\u1ee9 t\u1ef1 l\u00e0 giao \u0111i\u1ec3m th\u1ee9 hai c\u1ee7a c\u00e1c tia AH, BH, CH v\u1edbi \u0111\u01b0\u1eddng tr\u00f2n (O); A‘<\/sup>1<\/sub>, B‘<\/sup>1<\/sub>,C‘<\/sup>1<\/sub>\u00a0t\u01b0\u01a1ng \u1ee9ng l\u00e0 ch\u00e2n c\u00e1c \u0111\u01b0\u1eddng cao \u0111i qua A, B, C. T\u00ecm \u1ea3nh c\u1ee7a A, B, C,A1<\/sub>, B1<\/sub>,C1<\/sub>\u00a0qua ph\u00e9p v\u1ecb t\u1ef1 t\u00e2m H t\u1ec9 s\u1ed1 1\/2.<\/p>\n}}

(e) Ch\u1ee9ng minh ch\u00edn \u0111i\u1ec3m A^{‘<\/sup>, B‘<\/sup>,C‘<\/sup>,A”<\/sup>, B”<\/sup>,C”<\/sup>,A‘<\/sup>_{1<\/sub>, B‘<\/sup>1<\/sub>,C‘<\/sup>1<\/sub>\u00a0c\u00f9ng thu\u1ed9c m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n (\u0111\u01b0\u1eddng tr\u00f2n n\u00e0y g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng tr\u00f2n \u01a0-le c\u1ee7a tam gi\u00e1c ABC)<\/p>\n}}

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

(a) F l\u00e0 ph\u00e9p v\u1ecb t\u1ef1 t\u00e2m G, t\u1ec9 s\u1ed1 1\/2.<\/p>\n

(b) \u0110\u1ec3 \u00fd r\u1eb1ng O l\u00e0 tr\u1ef1c t\u00e2m c\u1ee7a tam gi\u00e1c A^{‘<\/sup>B‘<\/sup>C‘<\/sup><\/p>\n}

(c) F(O) = O_{1<\/sub>\u00a0l\u00e0 trung \u0111i\u1ec3m c\u1ee7a OH.<\/p>\n}

(d) \u1ea2nh c\u1ee7a A, B, C , A_{1<\/sub>, B1<\/sub>,C1<\/sub>\u00a0qua ph\u00e9p v\u1ecb t\u1ef1 t\u00e2m H t\u1ec9 s\u1ed1 1\/2 t\u01b0\u01a1ng \u1ee9ng l\u00e0 A^{”<\/sup>, B”<\/sup>,C”<\/sup>,A‘<\/sup>1<\/sub>, B‘<\/sup>1<\/sub>,C‘<\/sup>1<\/sub>.<\/p>\n}}

(e) Ch\u1ee9ng minh A^{”<\/sup>, B”<\/sup>,C”<\/sup>,A‘<\/sup>_{1<\/sub>, B‘<\/sup>1<\/sub>,C‘<\/sup>1<\/sub>\u00a0c\u00f9ng thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n (O1<\/sub>). Sau \u0111\u00f3 ch\u1ee9ng minh A‘<\/sup>B‘<\/sup>C‘<\/sup>\u00a0c\u0169ng thu\u1ed9c \u0111\u01b0\u1eddng tr\u00f2n (O1<\/sub>) . Ch\u1eb3ng h\u1ea1n , ch\u1ee9ng minh O1<\/sub>A‘<\/sup>1<\/sub>\u00a0= O1<\/sub>A‘<\/sup>B\u00e0i 3 (trang 126 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh ch\u00f3p S.ABCD c\u00f3 \u0111\u00e1y ABCD l\u00e0 h\u00ecnh thang v\u1edbi AB l\u00e0 \u0111\u00e1y l\u1edbn. G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n AB, E l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai c\u1ea1nh c\u1ee7a h\u00ecnh thang ABCD v\u00e0 G l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c ECD.<\/p>\n}}

(a) Ch\u1ee9ng minh r\u1eb1ng b\u1ed1n \u0111i\u1ec3m S, E, M, G c\u00f9ng thu\u1ed9c m\u1ed9t m\u1eb7t ph\u1eb3ng (\u03b1) v\u00e0 m\u1eb7t ph\u1eb3ng n\u00e0y c\u1eaft c\u1ea3 hai m\u1eb7t ph\u1eb3ng (SAC) v\u00e0 (SBD) theo c\u00f9ng m\u1ed9t giao tuy\u1ebfn d.<\/p>\n

(b) X\u00e1c \u0111\u1ecbnh giao tuy\u1ebfn c\u1ee7a hai m\u1eb7t ph\u1eb3ng (SAD) v\u00e0 (SBC).<\/p>\n

(c) L\u1ea5y m\u1ed9t \u0111i\u1ec3m K tr\u00ean \u0111o\u1ea1n SE v\u00e0 g\u1ecdi C^{‘<\/sup>\u00a0= SC \u2229KB, D‘<\/sup>=SD \u2229KA. Ch\u1ee9ng minh r\u1eb1ng hai giao \u0111i\u1ec3m c\u1ee7a AC‘<\/sup>\u00a0v\u00e0 BD‘<\/sup>\u00a0thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng d n\u00f3i tr\u00ean.<\/p>\n}

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

<\/p>\n

<\/p>\n

B\u00e0i 4 (trang 126 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh l\u0103ng tr\u1ee5 t\u1ee9 gi\u00e1c ABCD.A’B’C’D’ c\u00f3 E, F, M v\u00e0 N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AC, BD, AC’ v\u00e0 BD’. Ch\u1ee9ng minh MN = EF.<\/p>\n

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

<\/p>\n

B\u00e0i 5 (trang 126 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh l\u1eadp ph\u01b0\u01a1ng ABCD.A’B’C’D’ c\u00f3 E v\u00e0 F l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u00e1c c\u1ea1nh AB v\u00e0 \u0110’. H\u00e3y x\u00e1c \u0111\u1ecbnh c\u00e1c thi\u1ebft di\u1ec7n c\u1ee7a h\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u1eaft b\u1edfi c\u00e1c m\u1eb7t ph\u1eb3ng (EFB), (EFC), (EFC’) v\u00e0 (EFK) v\u1edbi K l\u00e0 trung \u0111i\u1ec3m c\u1ee7a c\u1ea1nh B’C’<\/p>\n

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

<\/p>\n

B\u00e0i 6 (trang 126 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh l\u1eadp ph\u01b0\u01a1ng ABCD.A’B’C’D’ c\u00f3 c\u1ea1nh b\u1eb1ng a.<\/p>\n

a) H\u00e3y x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c chung c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng ch\u00e9o nhau BD’ v\u00e0 B’C.<\/p>\n

b) T\u00ednh kho\u1ea3ng c\u00e1ch c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng BD’ v\u00e0 B’C<\/p>\n

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

<\/p>\n

<\/p>\n

B\u00e0i 7 (trang 126 SGK H\u00ecnh h\u1ecdc 11):<\/b>\u00a0Cho h\u00ecnh thang ABCD vu\u00f4ng t\u1ea1i A v\u00e0 B, c\u00f3 AD = 2a, AB = BC = a. Tr\u00ean tia Ax vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (ABCD) l\u1ea5y m\u1ed9t \u0111i\u1ec3m S. G\u1ecdi C^{‘<\/sup>, D‘<\/sup>\u00a0l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c ucar A tr\u00ean SC v\u00e0 SD . Ch\u1ee9ng minh r\u1eb1ng :<\/p>\n}

<\/p>\n

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

<\/p>\n

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

B\u00e0i 1 (trang 125 SGK H\u00ecnh h\u1ecdc 11):\u00a0Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, cho c\u00e1c \u0111i\u1ec3m A (1;1), B(0;3), C(2;4) .X\u00e1c \u0111\u1ecbnh \u1ea3nh c\u1ee7a tam gi\u00e1c ABC qua c\u00e1c ph\u00e9p bi\u1ebfn h\u00ecnh sau. (a)Ph\u00e9p t\u1ecbnh ti\u1ebfn theo vector v = (2;1). (b)Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua tr\u1ee5c Ox (c)Ph\u00e9p \u0111\u1ed1i x\u1ee9ng qua t\u00e2m I(2;1). (d)Ph\u00e9p quay […]<\/p>\n","protected":false},"author":3,"featured_media":29352,"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":"\n