Nguyễn Nhân Tình_chương 1_khối đa diện

["C\u00abng ty TNHH gi\u00b8o d\u00f4c t\u00e6ng h\u00eep Th\u00b5nh Nh\u00a9n H\u00d7nh h\u00e4c 12 \u2013 Ch\u00ad\u00acng 1. Kh\u00e8i \u00a7a Di\u00d6n Nh\u00f3m 2. Ph\u01b0\u01a1ng ph\u00e1p tr\u01b0\u1ee3t \u0111\u1ec9nh 40. Cho h\u00ecnh h\u1ed9p \u0111\u1ee9ng ABCD.A\uf0a2B\uf0a2C\uf0a2D\uf0a2 c\u00f3 AA\uf0a2 \uf03d AB \uf03d a, \u0111\u00e1y l\u00e0 h\u00ecnh thoi v\u00e0 B\uf0b7AD \uf03d 60\uf0b0. G\u1ecdi J , I l\u1ea7n l\u01b0\u1ee3t l\u00e0 t\u00e2m c\u1ee7a c\u00e1c h\u00ecnh vu\u00f4ng A\uf0a2B\uf0a2C\uf0a2D\uf0a2 v\u00e0 A\uf0a2D\uf0a2DA. G\u1ecdi K, L l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB, BC. Th\u1ec3 t\u00edch kh\u1ed1i ch\u00f3p IJKL b\u1eb1ng 6a3 3a3 3a3 3a3 A. \uf0d7 B. \uf0d7 C. \uf0d7 D. \uf0d7 12 16 12 24 ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ 41. Cho kh\u1ed1i l\u0103ng tr\u1ee5 tam gi\u00e1c ABC.A\uf0a2B\uf0a2C\uf0a2, g\u1ecdi G l\u00e0 tr\u1ecdng t\u00e2m tam gi\u00e1c ABC. G\u1ecdi M , N , P l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a CC\uf0a2, A\uf0a2C\uf0a2, A\uf0a2B\uf0a2. Bi\u1ebft th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i GMNP b\u1eb1ng 5. Th\u1ec3 t\u00edch kh\u1ed1i l\u0103ng tr\u1ee5 ABC.A\uf0a2B\uf0a2C\uf0a2 b\u1eb1ng A. 72. B. 21. C. 18. D. 17. ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ 42. Cho h\u00ecnh h\u1ed9p ABCD.A\uf0a2B\uf0a2C\uf0a2D\uf0a2. Tr\u00ean c\u1ea1nh BC l\u1ea5y \u0111i\u1ec3m M sao cho BM \uf03d 3MC. T\u00ednh VAB\uf0a2D\uf0a2M . VA\uf0a2BCD A. 13 \uf0d7 B. 1 \uf0d7 C. 7 \uf0d7 D. 1 \uf0d7 8 2 8 4 ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ 43. Cho kh\u1ed1i h\u1ed9p ch\u1eef nh\u1eadt ABCD.A\uf0a2B\uf0a2C\uf0a2D\uf0a2 c\u00f3 th\u1ec3 t\u00edch b\u1eb1ng 256. G\u1ecdi M , N , P l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a BC, C\uf0a2D\uf0a2, DD\uf0a2. Th\u1ec3 t\u00edch c\u1ee7a t\u1ee9 di\u1ec7n AMNP b\u1eb1ng A. 16. B. 18. C. 24. D. 12. ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ Bi\u00aan so\u00b9n & gi\u00b6ng d\u00b9y: Ths. Nguy\u00d4n Nh\u00a9n T\u00d7nh Trang 49","C\u00abng ty TNHH gi\u00b8o d\u00f4c t\u00e6ng h\u00eep Th\u00b5nh Nh\u00a9n H\u00d7nh h\u00e4c 12 \u2013 Ch\u00ad\u00acng 1. Kh\u00e8i \u00a7a Di\u00d6n Nh\u00f3m 3. Ph\u01b0\u01a1ng ph\u00e1p vu\u00f4ng g\u00f3c, tr\u01b0\u1ee3t \u0111\u1ec9nh 44. Cho h\u00ecnh ch\u00f3p S.ABC c\u00f3 \u0111\u00e1y l\u00e0 tam gi\u00e1c vu\u00f4ng t\u1ea1i A, c\u1ea1nh b\u00ean SA vu\u00f4ng g\u00f3c v\u1edbi \u0111\u00e1y, SA \uf03d BC. G\u1ecdi E, F l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a A l\u00ean SB, SC. M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a SA v\u00e0 G l\u00e0 tr\u1ecdng t\u00e2m tam gi\u00e1c ABC. T\u1ec9 s\u1ed1 VM .AEF b\u1eb1ng VG. AEF A. 3 \uf0d7 B. 3 \uf0d7 C. 2. D. 2 \uf0d7 2 2 2 ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ 45. Cho h\u00ecnh ch\u00f3p S.ABC c\u00f3 \u0111\u00e1y l\u00e0 tam gi\u00e1c vu\u00f4ng t\u1ea1i A, SA \uf03d 2BC v\u00e0 SA vu\u00f4ng g\u00f3c v\u1edbi \u0111\u00e1y. G\u1ecdi E, F l\u1ea7n l\u01b0\u1ee3t l\u00e0 h\u00ecnh chi\u1ebfu c\u1ee7a \u0111i\u1ec3m A l\u00ean SB, SC. M l\u00e0 trung \u0111i\u1ec3m c\u1ee7a SA, G l\u00e0 tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c ABC. T\u1ec9 s\u1ed1 VM .AEF b\u1eb1ng VG. AEF A. 1 \uf0d7 B. 6. C. 4. D. 3 \uf0d7 2 2 ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ Bi\u00aan so\u00b9n & gi\u00b6ng d\u00b9y: Ths. Nguy\u00d4n Nh\u00a9n T\u00d7nh Trang 50","C\u00abng ty TNHH gi\u00b8o d\u00f4c t\u00e6ng h\u00eep Th\u00b5nh Nh\u00a9n H\u00d7nh h\u00e4c 12 \u2013 Ch\u00ad\u00acng 1. Kh\u00e8i \u00a7a Di\u00d6n \u0110\u1ecbnh l\u00fd Talet D\u1ea1ng 7. Ph\u00e2n chia kh\u1ed1i \u0111a di\u1ec7n Nh\u00f3m 1. \u0110\u1ecbnh l\u00fd Menelauyt Ba \u0111i\u1ec3m M , N , L th\u1eb3ng h\u00e0ng th\u00ec: Ta c\u00f3: AB \uf050 EF th\u00ec: Ta c\u00f3: DE \uf050 BC th\u00ec: MA . LB . NC \uf03d 1. IA \uf03d IB \uf03d AB \uf0d7 AD \uf03d AE \uf03d DE \uf0d7 MB LC NA IF IE EF AB AC BC 46. [\u0110\u1ec0-TN-THPTQG-101-2019] Cho l\u0103ng tr\u1ee5 ABC.A\uf0a2B\uf0a2C\uf0a2 c\u00f3 chi\u1ec1u cao b\u1eb1ng 8 v\u00e0 \u0111\u00e1y l\u00e0 tam gi\u00e1c \u0111\u1ec1u c\u1ea1nh b\u1eb1ng 6. G\u1ecdi M , N v\u00e0 P l\u1ea7n l\u01b0\u1ee3t l\u00e0 t\u00e2m c\u1ee7a c\u00e1c m\u1eb7t b\u00ean ABB\uf0a2A\uf0a2, ACC\uf0a2A\uf0a2 v\u00e0 BCC\uf0a2B\uf0a2. Th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i \u0111a di\u1ec7n l\u1ed3i c\u00f3 c\u00e1c \u0111\u1ec9nh l\u00e0 c\u00e1c \u0111i\u1ec3m A, B, C, M , N , P b\u1eb1ng A. 27 3. B. 21 3. C. 30 3. D. 36 3. ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ 47. Cho h\u00ecnh ch\u00f3p t\u1ee9 di\u1ec7n \u0111\u1ec1u S.ABCD. G\u1ecdi M l\u00e0 \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng v\u1edbi C qua D, N l\u00e0 trung \u0111i\u1ec3m c\u1ee7a SC, m\u1eb7t ph\u1eb3ng \uf028 BMN \uf029 chia kh\u1ed1i ch\u00f3p S.ABCD th\u00e0nh hai ph\u1ea7n. T\u1ec9 s\u1ed1 th\u1ec3 t\u00edch c\u1ee7a hai ph\u1ea7n \u0111\u00f3 b\u1eb1ng B. 8 \uf0d7 C. 7 \uf0d7 D. 7 \uf0d7 A. 9 \uf0d7 5 6 5 5 ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ Bi\u00aan so\u00b9n & gi\u00b6ng d\u00b9y: Ths. Nguy\u00d4n Nh\u00a9n T\u00d7nh Trang 51","C\u00abng ty TNHH gi\u00b8o d\u00f4c t\u00e6ng h\u00eep Th\u00b5nh Nh\u00a9n H\u00d7nh h\u00e4c 12 \u2013 Ch\u00ad\u00acng 1. Kh\u00e8i \u00a7a Di\u00d6n 48. Cho h\u00ecnh ch\u00f3p t\u1ee9 di\u1ec7n \u0111\u1ec1u S.ABCD. G\u1ecdi M l\u00e0 \u0111i\u1ec3m \u0111\u1ed1i x\u1ee9ng v\u1edbi C qua D, N l\u00e0 trung \u0111i\u1ec3m c\u1ee7a SC, m\u1eb7t ph\u1eb3ng \uf028 BMN \uf029 chia kh\u1ed1i ch\u00f3p S.ABCD th\u00e0nh hai ph\u1ea7n. T\u1ec9 s\u1ed1 th\u1ec3 t\u00edch c\u1ee7a hai ph\u1ea7n b\u1eb1ng A. 9 \uf0d7 B. 8 \uf0d7 C. 7 \uf0d7 D. 7 \uf0d7 5 5 6 5 ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ 49. Cho kh\u1ed1i l\u0103ng tr\u1ee5 \u0111\u1ee9ng ABC.A\uf0a2B\uf0a2C\uf0a2 c\u00f3 th\u1ec3 t\u00edch b\u1eb1ng 3 3a3 . G\u1ecdi M , N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m 4 c\u1ee7a A\uf0a2C\uf0a2 v\u00e0 BC. M\u1eb7t ph\u1eb3ng \uf028 AMN \uf029 chia kh\u1ed1i l\u0103ng tr\u1ee5 th\u00e0nh hai ph\u1ea7n. Th\u1ec3 t\u00edch c\u1ee7a ph\u1ea7n nh\u1ecf b\u1eb1ng 7 3a3 7 3a3 7 3a3 D. 7a3 \uf0d7 A. \uf0d7 B. \uf0d7 C. \uf0d7 16 16 32 64 ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ 50. Cho kh\u1ed1i l\u1eadp ph\u01b0\u01a1ng ABCD.A\uf0a2B\uf0a2C\uf0a2D\uf0a2 c\u00f3 c\u1ea1nh b\u1eb1ng a. G\u1ecdi M l\u00e0 trung \u0111i\u1ec3m AA\uf0a2. M\u1eb7t ph\u1eb3ng \uf028 B\uf0a2MC \uf029 chia kh\u1ed1i l\u1eadp ph\u01b0\u01a1ng tr\u00ean th\u00e0nh hai ph\u1ea7n. Th\u1ec3 t\u00edch ph\u1ea7n ch\u1ee9a \u0111\u1ec9nh D b\u1eb1ng A. 7a3 \uf0d7 B. 5a3 \uf0d7 C. 17a3 \uf0d7 D. 7a3 \uf0d7 12 12 24 24 ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ ................................................................................................. ................................................................ Bi\u00aan so\u00b9n & gi\u00b6ng d\u00b9y: Ths. Nguy\u00d4n Nh\u00a9n T\u00d7nh Trang 52"]