SGV TOAN 8-CTST

["","","","","","","","","","","","","","","","","","","","","","","","","","","","","M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110KP 1: T\u00ednh di\u1ec7n t\u00edch c\u00e1c m\u1eb7t c\u1ee7a h\u00ecnh khai tri\u1ec3n r\u1ed3i c\u1ed9ng di\u1ec7n t\u00edch c\u00e1c m\u1eb7t b\u00ean ta \u0111\u01b0\u1ee3c di\u1ec7n t\u00edch xung quanh c\u1ee7a h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u. C\u00e1c y\u00eau c\u1ea7u t\u1eeb c\u00e2u a \u0111\u1ebfn c\u00e2u c l\u00e0 t\u1eebng b\u01b0\u1edbc x\u00e1c l\u1eadp c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch xung quanh: t\u00ecm s\u1ed1 m\u1eb7t b\u00ean, t\u00ednh di\u1ec7n t\u00edch m\u1ed7i m\u1eb7t, t\u00ednh t\u1ed5ng di\u1ec7n t\u00edch c\u1ee7a 4 m\u1eb7t b\u00ean \u0111\u00f3. C\u00e2u d y\u00eau c\u1ea7u t\u00ednh di\u1ec7n t\u00edch \u0111\u00e1y \u0111\u1ec3 t\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n. M\u1eb7c d\u00f9 ho\u1ea1t \u0111\u1ed9ng ch\u1ec9 \u0111\u1ec1 c\u1eadp \u0111\u1ebfn t\u00ednh di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u, nh\u01b0ng ph\u1ea7n ghi nh\u1edb t\u1ed5ng qu\u00e1t ho\u00e1 c\u00e1ch t\u00ednh di\u1ec7n t\u00edch xung quanh v\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a c\u1ea3 h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u v\u00e0 h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u. Th\u1ef1c h\u00e0nh 1. M\u1ed9t t\u1ea5m b\u00eca (H\u00ecnh 2) g\u1ea5p th\u00e0nh h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u v\u1edbi c\u00e1c m\u1eb7t \u0111\u1ec1u l\u00e0 h\u00ecnh tam gi\u00e1c \u0111\u1ec1u. V\u1edbi s\u1ed1 \u0111o tr\u00ean h\u00ecnh v\u1ebd, h\u00e3y t\u00ednh di\u1ec7n t\u00edch xung quanh v\u00e0 di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a h\u00ecnh n\u00e0y. 10 cm M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 1: Gi\u00fap HS luy\u1ec7n t\u1eadp t\u00ednh to\u00e1n v\u1edbi 8,7 cm c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch xung quanh, di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n trong H\u00ecnh 2 th\u1ef1c t\u1ebf, \u0111\u1ed3ng th\u1eddi bi\u1ebft quan s\u00e1t h\u00ecnh v\u1ebd \u0111\u1ec3 t\u00ecm ra th\u00f4ng tin \u0111\u1ec3 \u0111\u00e1p \u1ee9ng y\u00eau c\u1ea7u b\u00e0i to\u00e1n. \u0110\u1ed1i v\u1edbi b\u00e0i to\u00e1n h\u00ecnh h\u1ecdc, gi\u1ea3 thi\u1ebft c\u00f3 th\u1ec3 cho d\u01b0\u1edbi d\u1ea1ng v\u0103n b\u1ea3n thu\u1ea7n tu\u00fd ho\u1eb7c c\u1ea3 v\u0103n b\u1ea3n v\u00e0 h\u00ecnh v\u1ebd. 2. Th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u v\u00e0 h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u H\u0110KP 2 78","\u2013 M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110KP 2: Gi\u00fap HS l\u00e0m quen v\u1edbi vi\u1ec7c x\u00e2y d\u1ef1ng c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch m\u1ed9t h\u00ecnh d\u1ef1a v\u00e0o nh\u1eefng h\u00ecnh \u0111\u00e3 bi\u1ebft \u0111\u01b0\u1ee3c c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch. Ho\u1ea1t \u0111\u1ed9ng n\u00e0y tr\u00ecnh b\u00e0y m\u1ed9t th\u00ed nghi\u1ec7m \u0111\u1ec3 d\u1eabn \u0111\u1ebfn c\u00f4ng th\u1ee9c t\u00ednh. N\u1ebfu c\u00f3 \u0111i\u1ec1u ki\u1ec7n l\u00e0m ho\u1ea1t \u0111\u1ed9ng tr\u1ea3i nghi\u1ec7m th\u00ec ti\u1ebft d\u1ea1y s\u1ebd hi\u1ec7u qu\u1ea3 h\u01a1n. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c H\u0110KP 2: GV ch\u00fa \u00fd \u0111i\u1ec1u ki\u1ec7n c\u1ee7a c\u00e1i g\u00e0u v\u00e0 c\u00e1i th\u00f9ng ph\u1ea3i c\u00f3 c\u00f9ng di\u1ec7n t\u00edch \u0111\u00e1y v\u00e0 chi\u1ec1u cao. Th\u1ef1c ch\u1ea5t ch\u00ednh l\u00e0 hai h\u00ecnh c\u00f3 c\u00f9ng di\u1ec7n t\u00edch \u0111\u00e1y v\u00e0 chi\u1ec1u cao. Th\u1ec3 t\u00edch n\u01b0\u1edbc theo th\u00ed nghi\u1ec7m ch\u00ednh b\u1eb1ng di\u1ec7n t\u00edch \u0111\u00e1y nh\u00e2n v\u1edbi chi\u1ec1u cao c\u1ed9t n\u01b0\u1edbc khi \u0111\u1ed5 v\u00e0o th\u00f9ng h\u00ecnh l\u0103ng tr\u1ee5 \u0111\u1ee9ng l\u00e0 S = 1 .S\u0111\u00e1y . h. \u0110\u00f3 ch\u00ednh l\u00e0 th\u1ec3 t\u00edch c\u1ee7a h\u00ecnh ch\u00f3p. 3 Th\u00ed nghi\u1ec7m ch\u1ec9 t\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u, nh\u01b0ng t\u1ed5ng qu\u00e1t cho t\u00ednh th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p n\u00f3i chung. Th\u1ef1c h\u00e0nh 2. T\u00ednh th\u1ec3 t\u00edch c\u1ee7a m\u00f4\u0323t chi\u1ebfc h\u1ed9p b\u00e1nh \u00edt co\u0301 H\u00ecnh 6 da\u0323ng h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u, c\u00f3 \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u00e1y l\u00e0 3 cm v\u00e0 chi\u1ec1u cao l\u00e0 2,5 cm. M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 2: Gi\u00fap HS t\u00ednh to\u00e1n v\u1edbi nh\u1eefng v\u1eadt th\u1ec3 c\u00f3 d\u1ea1ng h\u00ecnh h\u1ecdc quen thu\u1ed9c trong \u0111\u1eddi s\u1ed1ng, c\u1ee5 th\u1ec3 \u1edf \u0111\u00e2y l\u00e0 t\u00ednh th\u1ec3 t\u00edch c\u1ee7a h\u1ed9p b\u00e1nh \u00edt. \u0110\u00e2y l\u00e0 b\u00e0i to\u00e1n t\u00edch h\u1ee3p, li\u00ean h\u1ec7 gi\u1eefa h\u00ecnh h\u1ecdc v\u00e0 \u0111\u1eb7c s\u1ea3n c\u1ee7a Vi\u1ec7t Nam, gi\u00fap h\u1ecdc sinh li\u00ean h\u1ec7 to\u00e1n h\u1ecdc v\u1edbi cu\u1ed9c s\u1ed1ng. Th\u1ef1c h\u00e0nh 3. H\u00e3y gi\u1ea3i b\u00e0i to\u00e1n \u01a1\u0309 ph\u00e2\u0300n (trang 49). \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 3: Nh\u1eafc l\u1ea1i c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u, h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u, \u0111\u1ed3ng th\u1eddi th\u1ea5y s\u1ef1 li\u00ean h\u1ec7 c\u1ee7a th\u1ec3 t\u00edch h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u, h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u v\u1edbi h\u00ecnh l\u0103ng tr\u1ee5 t\u01b0\u01a1ng \u1ee9ng. \u2013 G\u1ee3i \u00fd t\u1ed5 ch\u1ee9c Th\u1ef1c h\u00e0nh 3: GV c\u00f3 th\u1ec3 cho c\u00e1c t\u1ed5 th\u1ef1c h\u00e0nh v\u00e0 t\u1ed5ng k\u1ebft. V\u1eadn d\u1ee5ng 1. M\u1ed9t chi\u1ebfc l\u1ec1u co\u0301 da\u0323ng h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u \u1edf tr\u1ea1i h\u00e8 c\u1ee7a h\u1ecdc sinh c\u00f3 k\u00edch th\u01b0\u1edbc nh\u01b0 H\u00ecnh 7. a) T\u00ednh th\u1ec3 t\u00edch kh\u00f4ng kh\u00ed trong chi\u1ebfc l\u1ec1u. b) T\u00ednh di\u1ec7n t\u00edch v\u1ea3i l\u1ec1u (kh\u00f4ng t\u00ednh c\u00e1c m\u00e9p d\u00e1n), bi\u1ebft 2,8 m chi\u1ec1u cao c\u1ee7a m\u1eb7t b\u00ean xu\u1ea5t ph\u00e1t t\u1eeb \u0111\u1ec9nh c\u1ee7a chi\u00ea\u0301c l\u00ea\u0300u l\u00e0 3,18 m v\u00e0 l\u1ec1u n\u00e0y kh\u00f4ng c\u00f3 \u0111\u00e1y. M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng 1: T\u00ednh th\u1ec3 t\u00edch c\u1ee7a chi\u1ebfc l\u1ec1u \u0111\u1ec3 3m d\u1ef1 \u0111o\u00e1n s\u1ed1 ng\u01b0\u1eddi \u1edf trong l\u1ec1u cho th\u00edch h\u1ee3p, ngo\u00e0i ra c\u0169ng H\u00ecnh 7 t\u00ednh di\u1ec7n t\u00edch xung quanh \u0111\u1ec3 khi c\u1ea7n c\u00f3 th\u1ec3 t\u00ednh to\u00e1n chi ph\u00ed cho vi\u1ec7c may chi\u1ebfc l\u1ec1u. 79","V\u1eadn d\u1ee5ng 2. M\u1ed9t b\u1ec3 k\u00ednh h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt c\u00f3 hai c\u1ea1nh \u0111\u00e1y l\u00e0 60 cm v\u00e0 30 cm. Trong b\u1ec3 c\u00f3 m\u1ed9t kh\u1ed1i \u0111\u00e1 h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u v\u1edbi di\u1ec7n ? t\u00edch \u0111\u00e1y l\u00e0 270 cm2, chi\u1ec1u cao 60 cm H\u00ecnh 8 30 cm. Ng\u01b0\u1eddi ta \u0111\u1ed5 n\u01b0\u1edbc v\u00e0o b\u00ea\u0309 sao cho n\u01b0\u01a1\u0301c ng\u1eadp kh\u1ed1i \u0111\u00e1 v\u00e0 \u0111o \u0111\u01b0\u1ee3c m\u1ef1c n\u01b0\u1edbc l\u00e0 60 cm. a) b) Khi l\u1ea5y kh\u1ed1i \u0111\u00e1 ra th\u00ec m\u1ef1c n\u01b0\u1edbc c\u1ee7a b\u1ec3 l\u00e0 bao nhi\u00eau? Bi\u1ebft r\u1eb1ng b\u1ec1 d\u00e0y c\u1ee7a \u0111\u00e1y b\u1ec3 v\u00e0 th\u00e0nh b\u1ec3 kh\u00f4ng \u0111\u00e1ng k\u1ec3. M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng 2: V\u1eadn d\u1ee5ng c\u00f4ng th\u1ee9c t\u00ednh th\u1ec3 t\u00edch \u0111\u1ec3 gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n th\u1ef1c t\u1ebf t\u00ednh m\u1ef1c n\u01b0\u1edbc sau khi b\u1ecf h\u00f2n \u0111\u00e1 v\u00e0o. GV c\u00f3 th\u1ec3 thay \u0111\u1ed5i d\u1eef ki\u1ec7n v\u00e0 \u0111\u1ec1 b\u00e0i \u0111\u1ec3 b\u00e0i to\u00e1n phong ph\u00fa \u0111a d\u1ea1ng h\u01a1n. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: Th\u1ec3 t\u00edch kh\u1ed1i \u0111\u00e1 h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u l\u00e0 V = 1 . S\u0111\u00e1y . h = 1 . 270 . 30 = 2 700 (cm3). 3 3 Chi\u1ec1u cao m\u1ef1c n\u01b0\u1edbc b\u1ecb h\u1ee5t \u0111i l\u00e0 h = V : S\u0111\u00e1y b\u1ec3 = 2700 : (60 . 30) = 2700 : 1800 = 1,5 (cm). M\u1ef1c n\u01b0\u1edbc c\u1ee7a b\u1ec3 l\u00e0 60 \u2013 1,5 = 58,5 (cm). IV. H\u01b0\u1edbng d\u1eabn gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp 1. \ta) H\u00ecnh a): Sxq = 4 \u22c5 5.6 = 60 (cm2); H\u00ecnh b): Sxq = 4 \u22c513.10 = 260 (cm2); 2 2 b) H\u00ecnh a): V = 1 . S\u0111\u00e1y . h = 1 . (6 . 6) . 4 = 48 (cm3); 3 3 11 . (10 . 10) . 12 = 400 (cm3). H\u00ecnh b): V = 3 . S\u0111\u00e1y . h = 3 2. \tDi\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a chi\u1ebfc l\u1ed3ng \u0111\u00e8n h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u l\u00e0: Stp = Sxq + S\u0111\u00e1y = 4 \u22c5 30 . 40 + 30 . 30 = 3 300 (cm2). 2 S\u1ed1 m\u00e9t vu\u00f4ng gi\u1ea5y c\u1ea7n c\u00f3: 3300 cm2 = 0,33 m2. 3. \ta) Sxq = 3 \u22c512.10 = 180 (cm2); 2 72.77 b) Stp = Sxq + S\u0111\u00e1y = 4 \u22c5 2 + 72 . 72 = 16 272 (dm2); V = 1 . S\u0111\u00e1y . h = 1 . 72 . 72 . 68,1 = 117 676,8 (dm3). 3 3 4. \tTh\u1ec3 t\u00edch kim t\u1ef1 th\u00e1p \u1edf b\u1ea3o t\u00e0ng Louvre l\u00e0: \tV= 1 . S\u0111\u00e1y . h = 1 . (34 . 34) . 21,3 = 8 2 07,6 (m3). 3 3 80","B\u00c0I T\u1eacP CU\u1ed0I CH\u01af\u01a0NG 2 C\u00c2U H\u1eceI TR\u1eaeC NGHI\u1ec6M 1. D 2. C 3. D 4. D 5. A B\u00c0I T\u1eacP T\u1ef0 LU\u1eacN 6. \tT\u1ea5m b\u00eca \u1edf H\u00ecnh 1a g\u1ea5p \u0111\u01b0\u1ee3c h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u; T\u1ea5m b\u00eca \u1edf H\u00ecnh 1c g\u1ea5p \u0111\u01b0\u1ee3c h\u00ecnh ch\u00f3p t\u1ee9 gi\u00e1c \u0111\u1ec1u. 7. \tH\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u \u1edf H\u00ecnh 2 c\u00f3: a) M l\u00e0 \u0111\u1ec9nh; c\u00e1c m\u1eb7t b\u00ean l\u00e0: MAB, MBC, MAC; b) MA = 17 cm; BC = 13 cm; c) MO l\u00e0 \u0111\u01b0\u1eddng cao. 8. \tH\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u \u1edf H\u00ecnh 3 c\u00f3: a) M\u1eb7t \u0111\u00e1y l\u00e0 ABCD; c\u00e1c m\u1eb7t b\u00ean l\u00e0: IAB, IBC, ICD, IDA; b) IB = 18 cm; BC = 14 cm; c) IH l\u00e0 \u0111\u01b0\u1eddng cao. 9. \ta) Sxq = 3 \u22c5 40.99 = 5 940 (cm2). 2 Stp = Sxq + S\u0111\u00e1y = 5940 + 1 . 40 . 34,6 = 6 632 (cm2); 2 11 1 . 40 . 34,6 . 98,3 \u2248 22 674,53 (cm3). V = 3 . S\u0111\u00e1y . h = 3 . 2 b) Sxq = 4 \u22c5120.91 = 21 840 (cm2). 2 Stp = Sxq + S\u0111\u00e1y = 21840 + 120 . 120 = 36 240 (cm2); \t V = 1 . S\u0111\u00e1y . h = 1 . 120 . 120 . 68,4 = 328 320 (cm3). 3 3 10. \tV = 1 . S\u0111\u00e1y . h = 1 . 1 . 6 . 3 3.2 6 \u2248 25,46 (cm3). 3 3 2 11. Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a m\u1ed7i chi\u1ebfc h\u1ed9p l\u00e0 Stp = 4 \u22c5 5. 4, 3 = 43 (cm2). 2 Di\u1ec7n t\u00edch to\u00e0n ph\u1ea7n c\u1ee7a 100 h\u1ed9p qu\u00e0 l\u00e0 43 . 100 = 4 300 (cm2). Di\u1ec7n t\u00edch gi\u1ea5y c\u1ea7n \u0111\u1ec3 g\u1ea5p 100 h\u1ed9p qu\u00e0 l\u00e0 4300.120 = 5 160 (cm2). 100 12. Th\u1ec3 t\u00edch c\u1ee7a kh\u1ed1i \u0111\u00e1 l\u00e0 V = 1 . 20 . 20 . 15 = 2000 (cm2). 3 Chi\u1ec1u cao c\u1ee7a m\u1ef1c n\u01b0\u1edbc t\u0103ng th\u00eam l\u00e0 2000 : (50 . 40) = 1 (cm). Kho\u1ea3ng c\u00e1ch t\u1eeb m\u1ef1c n\u01b0\u1edbc t\u1edbi mi\u1ec7ng b\u00ecnh l\u00e0 15 \u2013 1 = 14 (cm). 81","H\u00ccNH H\u1eccC PH\u1eb2NG Ch\u01b0\u01a1ng 3 \u0110\u1ecaNH L\u00cd PYTHAGORE. C\u00c1C LO\u1ea0I T\u1ee8 GI\u00c1C TH\u01af\u1edcNG G\u1eb6P A. M\u1ee4C TI\u00caU 1. N\u0103ng l\u01b0\u0323c chuy\u00ean m\u00f4n \u2013 \u0110\u1ecbnh l\u00ed Pythagore: Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c \u0111\u1ecbnh l\u00ed Pythagore. T\u00ednh \u0111\u01b0\u1ee3c \u0111\u1ed9 d\u00e0i c\u1ea1nh trong tam gi\u00e1c vu\u00f4ng b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed Pythagore. Gi\u1ea3i quy\u1ebft \u0111\u01b0\u1ee3c m\u00f4\u0323t s\u00f4\u0301 v\u1ea5n \u0111\u1ec1 th\u01b0\u0323c ti\u00ea\u0303n li\u00ean quan \u0111\u1ebfn \u0111\u1ecbnh l\u00ed Pythagore. \u2013 T\u1ee9 gi\u00e1c: M\u00f4 t\u1ea3 \u0111\u01b0\u1ee3c t\u1ee9 gi\u00e1c, t\u1ee9 gi\u00e1c l\u1ed3i. Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c \u0111\u1ecbnh l\u00ed v\u1ec1 t\u1ed5ng c\u00e1c g\u00f3c trong m\u1ed9t t\u1ee9 gi\u00e1c l\u1ed3i b\u1eb1ng 360o. \u2013 H\u00ecnh thang, h\u00ecnh thang c\u00e2n: Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c t\u00ednh ch\u1ea5t v\u1ec1 g\u00f3c k\u1ec1 m\u1ed9t \u0111\u00e1y, c\u1ea1nh b\u00ean, \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh thang c\u00e2n. Nh\u1eadn bi\u1ebft \u0111\u01b0\u1ee3c d\u1ea5u hi\u1ec7u \u0111\u1ec3 m\u1ed9t h\u00ecnh thang l\u00e0 m\u1ed9t h\u00ecnh thang c\u00e2n. \u2013 H\u00ecnh b\u00ecnh h\u00e0nh: Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c t\u00ednh ch\u1ea5t v\u1ec1 c\u1ea1nh \u0111\u1ed1i, g\u00f3c \u0111\u1ed1i, \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh. Nh\u1eadn bi\u1ebft \u0111\u01b0\u1ee3c d\u1ea5u hi\u1ec7u \u0111\u1ec3 m\u1ed9t t\u1ee9 gi\u00e1c l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh. \u2013 H\u00ecnh ch\u1eef nh\u1eadt: Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c t\u00ednh ch\u1ea5t v\u1ec1 hai \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh ch\u1eef nh\u1eadt. Nh\u1eadn bi\u1ebft \u0111\u01b0\u1ee3c d\u1ea5u hi\u1ec7u \u0111\u1ec3 m\u1ed9t h\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 h\u00ecnh ch\u1eef nh\u1eadt. \u2013 H\u00ecnh thoi: Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c t\u00ednh ch\u1ea5t v\u1ec1 \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh thoi. Nh\u1eadn bi\u1ebft \u0111\u01b0\u1ee3c d\u1ea5u hi\u1ec7u \u0111\u1ec3 m\u1ed9t h\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 h\u00ecnh thoi. \u2013 H\u00ecnh vu\u00f4ng: Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c t\u00ednh ch\u1ea5t v\u1ec1 hai \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh vu\u00f4ng. Nh\u1eadn bi\u1ebft \u0111\u01b0\u1ee3c d\u1ea5u hi\u1ec7u \u0111\u1ec3 m\u1ed9t h\u00ecnh ch\u1eef nh\u1eadt l\u00e0 h\u00ecnh vu\u00f4ng. 2. N\u0103ng l\u01b0\u0323c chung \u2013 N\u0103ng l\u01b0\u0323c t\u01b0\u0323 chu\u0309 va\u0300 t\u01b0\u0323 ho\u0323c trong ti\u0300m to\u0300i, kha\u0301m pha\u0301. \u2013 N\u0103ng l\u01b0\u0323c giao ti\u00ea\u0301p va\u0300 h\u01a1\u0323p ta\u0301c trong tri\u0300nh ba\u0300y, tha\u0309o lu\u00e2\u0323n va\u0300 la\u0300m vi\u00ea\u0323c nho\u0301m. \u2013 N\u0103ng l\u01b0\u0323c gia\u0309i quy\u00ea\u0301t v\u00e2\u0301n \u0111\u00ea\u0300 va\u0300 sa\u0301ng ta\u0323o trong th\u01b0\u0323c ha\u0300nh va\u0300 v\u00e2\u0323n du\u0323ng. 3. Hi\u0300nh tha\u0300nh ca\u0301c ph\u00e2\u0309m ch\u00e2\u0301t \u2013 Y\u00eau n\u01b0\u01a1\u0301c, nh\u00e2n \u00e1i. \u2013 Ch\u0103m chi\u0309, trung th\u01b0\u0323c, tra\u0301ch nhi\u00ea\u0323m. 82","B. H\u01af\u1edaNG D\u1eaaN D\u1ea0Y H\u1eccC B\u00e0i 1. \u0110\u1ecaNH L\u00cd PYTHAGORE I. M\u1ee5c ti\u00eau 1. Y\u00eau c\u1ea7u c\u00e2\u0300n \u0111a\u0323t: \u2013 Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c \u0111\u1ecbnh l\u00ed Pythagore. \u2013 T\u00ednh \u0111\u01b0\u1ee3c \u0111\u1ed9 d\u00e0i c\u1ea1nh trong tam gi\u00e1c vu\u00f4ng b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng \u0111\u1ecbnh l\u00ed Pythagore. \u2013 Gi\u1ea3i quy\u1ebft \u0111\u01b0\u1ee3c m\u1ed9t s\u1ed1 v\u1ea5n \u0111\u1ec1 th\u1ef1c ti\u1ec5n g\u1eafn v\u1edbi vi\u1ec7c v\u1eadn d\u1ee5ng \u0111\u1ecbnh l\u00ed Pythagore. 2. N\u0103ng l\u1ef1c ch\u00fa tr\u1ecdng: t\u01b0 duy v\u00e0 l\u1eadp lu\u1eadn to\u00e1n h\u1ecdc, m\u00f4 h\u00ecnh ho\u00e1 to\u00e1n h\u1ecdc, giao ti\u00ea\u0301p toa\u0301n ho\u0323c. 3. T\u00edch h\u1ee3p: To\u00e1n h\u1ecdc v\u00e0 cu\u1ed9c s\u1ed1ng, t\u00edch h\u1ee3p c\u00e1c m\u00f4n h\u1ecdc kh\u00e1c. II. M\u1ed9t s\u1ed1 ch\u00fa \u00fd 1. HS ghi nh\u1edb v\u00e0 n\u1eafm v\u1eefng \u0111\u01b0\u1ee3c \u0111\u1ecbnh l\u00ed Pythagore v\u00e0 \u0111\u1ecbnh l\u00ed Pythagore \u0111\u1ea3o. 2. C\u1ea7n y\u00eau c\u1ea7u HS gi\u1ea3i quy\u1ebft \u0111\u01b0\u1ee3c m\u00f4\u0323t s\u00f4\u0301 v\u1ea5n \u0111\u1ec1 th\u01b0\u0323c ti\u00ea\u0303n g\u1eafn v\u1edbi vi\u1ec7c v\u1eadn d\u1ee5ng \u0111\u1ecbnh l\u00ed Pythagore (v\u00ed d\u1ee5: t\u00ednh kho\u1ea3ng c\u00e1ch gi\u1eefa hai v\u1ecb tr\u00ed). III. G\u1ee3i \u00fd c\u00e1c ho\u1ea1t \u0111\u1ed9ng c\u1ee5 th\u1ec3 H\u0110K\u0110 B H\u00e3y so s\u00e1nh di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng m\u00e0u xanh 45 A v\u1edbi t\u1ed5ng di\u1ec7n t\u00edch c\u1ee7a hai h\u00ecnh vu\u00f4ng m\u00e0u \u0111\u1ecf v\u00e0 m\u00e0u v\u00e0ng. 3 C \u2013 M\u1ee5c \u0111\u00edch cu\u0309a H\u0110K\u0110: Gi\u00fap HS co\u0301 c\u01a1 h\u00f4\u0323i ph\u00e1t hi\u1ec7n \u0111\u1ecbnh l\u00ed Pythagore th\u00f4ng qua vi\u1ec7c so s\u00e1nh di\u1ec7n t\u00edch c\u00e1c h\u00ecnh vu\u00f4ng c\u00f3 c\u1ea1nh l\u00e0 c\u00e1c c\u1ea1nh c\u1ee7a tam gi\u00e1c vu\u00f4ng. C\u00e1ch \u0111\u1eb7t v\u1ea5n \u0111\u1ec1 n\u00e0y c\u00f3 kh\u1ea3 n\u0103ng thu h\u00fat HS v\u00e0o b\u00e0i h\u1ecdc. \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c H\u0110K\u0110: GV n\u00eau c\u00e2u h\u1ecfi, HS tra\u0309 l\u01a1\u0300i, l\u01a1\u0301p nh\u1eadn x\u00e9t, GV s\u1eed d\u1ee5ng c\u01a1 h\u1ed9i \u0111\u1ec3 gi\u1edbi thi\u1ec7u b\u00e0i. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: Di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng m\u00e0u xanh b\u1eb1ng t\u1ed5ng di\u1ec7n t\u00edch hai h\u00ecnh vu\u00f4ng m\u00e0u \u0111\u1ecf v\u00e0 m\u00e0u v\u00e0ng. L\u01b0u \u00fd: \u0110\u00e2y l\u00e0 c\u00e2u h\u1ecfi m\u1edf, t\u1ea1o s\u1ef1 ch\u00fa \u00fd v\u00e0 k\u1ebft n\u1ed1i. GV kh\u00f4ng c\u1ea7n \u0111\u00e1nh gi\u00e1 c\u00e2u tr\u1ea3 l\u1eddi c\u1ee7a HS \u0111\u00fang hay sai. Tinh th\u1ea7n chung c\u1ee7a H\u0110K\u0110 l\u00e0: \u201cM\u1ecdi c\u00e2u tr\u1ea3 l\u1eddi \u0111\u1ec1u \u0111\u01b0\u1ee3c ghi nh\u1eadn, mu\u1ed1n bi\u1ebft \u0111\u00fang \u2013 sai, h\u1ecdc xong b\u00e0i n\u00e0y s\u1ebd r\u00f5!\u201d. 83","1. \u0110\u1ecbnh l\u00ed Pythagore H\u0110KP 1 \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110KP 1: Gi\u00fap HS co\u0301 c\u01a1 h\u00f4\u0323i tr\u1ea3i nghi\u1ec7m, tha\u0309o lu\u00e2\u0323n v\u1ec1 c\u00e1ch gi\u1ea3i th\u00edch \u0111\u1ecbnh l\u00ed Pythagore. \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c H\u0110KP 1: GV n\u00eau c\u00e2u h\u1ecfi, HS tra\u0309 l\u01a1\u0300i, l\u01a1\u0301p nh\u1eadn x\u00e9t, GV \u0111a\u0301nh gia\u0301. GV c\u00f3 th\u1ec3 t\u1ed5 ch\u1ee9c cho HS l\u00e0m vi\u1ec7c nh\u00f3m ho\u1eb7c thuy\u1ebft tr\u00ecnh. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: a2 + b2 = c2. Th\u1ef1c h\u00e0nh 1. T\u00ednh \u0111\u1ed9 d\u00e0i c\u1ea1nh EF, MN c\u1ee7a c\u00e1c tam gi\u00e1c vu\u00f4ng trong H\u00ecnh 3. D 12 cm M 3 cm 5 cm ? P E? FN 4 cm a) b) H\u00ecnh 3 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 1: HS th\u01b0\u0323c ha\u0300nh t\u00ecm \u0111\u1ed9 d\u00e0i c\u1ea1nh th\u1ee9 ba c\u1ee7a m\u1ed9t tam gi\u00e1c vu\u00f4ng khi bi\u1ebft \u0111\u1ed9 d\u00e0i hai c\u1ea1nh \u0111\u1ec3 r\u00e8n luy\u1ec7n k\u0129 n\u0103ng theo y\u00eau c\u1ea7u c\u1ea7n \u0111\u1ea1t. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: a) EF = 13 cm; b) MN = 7 cm. H\u00ecnh 4 V\u1eadn d\u1ee5ng 1. M\u1ed9t chi\u1ebfc ti vi m\u00e0n h\u00ecnh ph\u1eb3ng c\u00f3 chi\u1ec1u r\u1ed9ng v\u00e0 chi\u1ec1u d\u00e0i \u0111o \u0111\u01b0\u1ee3c l\u1ea7n l\u01b0\u1ee3t l\u00e0 72 cm v\u00e0 120 cm. T\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a m\u00e0n h\u00ecnh chi\u1ebfc ti vi \u0111\u00f3 theo \u0111\u01a1n v\u1ecb inch (bi\u1ebft 1 inch \u2248 2,54 cm). 84","D 12 cm M 3 cm 5 cm ? P E? FN 4 cm \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng 1a:)HS c\u00f3 c\u01a1 h\u1ed9i v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c v\u1eeba h\u1ecdb)c v\u00e0o th\u1ef1c t\u1ebf s\u01b0\u0309 du\u0323ng \u0111\u1ecbnh l\u00ed Pythagore \u0111\u1ec3 t\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng ch\u00e9o Hc\u1ee7\u00ecnahm3 \u00e0n h\u00ecnh tivi khi bi\u1ebft hai k\u00edch th\u01b0\u1edbc. \u2013 G\u01a1V\u0323i\u1eady\u0301nt\u00f4d\u0309\u1ee5cnh\u01b0g\u0301c1V. M\u1eadn\u1ed9dt \u1ee5cnhgi\u1ebfc1:tiHvSi tmra\u00e0\u0309 nl\u01a1\u0300hi\u00ecyn\u00eahupch\u1ea7\u1eb3ungv\u00e0co\u00f3 v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. chi\u1ec1u r\u1ed9ng v\u00e0 chi\u1ec1u d\u00e0i \u0111o \u0111\u01b0\u1ee3c l\u1ea7n l\u01b0\u1ee3t l\u00e0 72 cm H\u01b0\u1edbvn\u00e0g1d2\u1eab0nc\u2013m\u0111. \u00e1Tp\u00edn\u00e1hn\u0111:\u1ed9 d7\u00e0i2\u01112 \u01b0+\u1edd1n2g0c2h\u2248\u00e9o13c\u1ee79a,9m4 \u00e0(ncmh\u00ec)n\u2248h 55,09 (inch). chi\u1ebfc ti vi \u0111\u00f3 theo \u0111\u01a1n v\u1ecb inch (bi\u1ebft 1 inch \u2248 2,54 cm). 2. \u0110\u1ecbnh l\u00ed Pythagore \u0111\u1ea3o H2.\u0110K\u0110P\u1ecaN2 H L\u00cd PYTHAGORE \u0110\u1ea2O H\u00ecnh 4 V\u1ebd v\u00e0o v\u1edf tam gi\u00e1c ABC c\u00f3 AB = 12 cm, AC = 5 cm, BC = 13 cm, r\u1ed3i x\u00e1c \u0111\u1ecbnh s\u1ed1 \u0111o 2 B\uf0b7AC b\u0103\u0300ng th\u01b0\u01a1\u0301c \u0111o g\u00f3c. \u2013 MKu\u0323chi\u0111bi\u0301ci\u1ebfht \u0111c\u1ed9u\u0309ad\u00e0Hi b\u0110aKcP\u1ea1n2h:cG\u1ee7ai\u00famp\u1ed9Ht tSaml\u00e0gmi\u00e1cq,uteanc\u00f3v\u1edbthi\u1ec3\u0111k\u1ecbin\u1ec3hmlt\u00edraPyxethmagtaomreg\u0111i\u00e1\u1ea3co\u0111q\u00f3uca\u00f3vpih\u1ec7\u1ea3ci nh\u1eadn bil\u1ebf\u00e0ttamm\u1ed9tgit\u00e1acmvug\u00f4i\u00e1ncgvkuh\u00f4\u00f4nngg nkhh\u1eddi bvi\u00e0\u1ebfot \u0111\u0111\u1ecb\u1ed9nhdl\u00e0\u00edisbaau:c\u1ea1nh c\u1ee7a m\u1ed9t tam gi\u00e1c. \u2013 G\u01a1\u0110\u0323i \u1ecbyn\u0301 ht\u00f4\u0309l\u00edchP\u01b0y\u0301cthHag\u0110oKreP\u01112\u1ea3:oG: V n\u00eau c\u00e2u h\u1ecfi, HS tra\u0309 l\u01a1\u0300i, l\u01a1\u0301p nh\u1eadn x\u00e9t, GV \u0111a\u0301nh gia\u0301. Th\u1ef1cN\u0111\u1ed9h\u1ebfu\u00e0dn\u00e0mih\u1ed9c2\u1ee7t a.taThm\u00ecamigcit\u1ea1\u00e1ancmhcg\u00f3kiib\u00e1ac\u00ectnhvh\u00ecutp\u00f4ahnm\u01b0g\u01a1gtnir\u00e1ogcn\u0111\u0111g\u1ed9\u00f3cdl\u00e1\u00e0\u00e0cittacam\u1ee7magmgi\u00e1i\u1ed9\u00e1ctcvcsu\u1ea1a\u00f4nunh:gb. \u0103\u0300ng t\u1ed5ng c\u00e1c b\u00ecnh ph\u01b0\u01a1ng a) Tam gi\u00e1c EFK c\u00f3 EF = 9 m, FK = 12 m, EK = 15 m. A b) TamGgTi\u00e1c P\u2206QARBCc\u00f3, BPCQ2 = A17Bc2 m+ ,AQCR2 = 12 cm, PR = 10 cm. c) TamKgLi\u00e1c DA\uf0b5E=F9c0\u00f3o DE = 8 m, DF = 6 m, EF = 10 m. \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 2: HS th\u01b0\u0323c ha\u0300nh nh\u1eadn d\u1ea1ng tamB gi\u00e1c vHu\u00ec\u00f4nnhg5 khi biC\u1ebft \u0111\u1ed9 d\u00e0i c\u1ea1nh c\u1ee7a tam gi\u00e1c \u0111\u1ec3 r\u00e8n luy\u1ec7n k\u0129 n\u0103ng theo y\u00eau c\u1ea7u c\u1ea7n \u0111\u1ea1t. 59 ba \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c Th\u1ef1c h\u00e0nh 2: HS tra\u0309 l\u01a1\u0300i y\u00eau c\u1ea7u v\u00e0o v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. V\u1eadn d\u1ee5ng 2. a) Nam d\u1ef1 \u0111\u1ecbnh l\u00e0m m\u1ed9t c\u00e1i \u00eake t\u1eeb ba thanh n\u1eb9p g\u1ed7. B C Nam \u0111\u00e3 c\u00f3 hai thanh l\u00e0m hai c\u1ea1nh g\u00f3c vu\u00f4ng d\u00e0i 6 cm A D v\u00e0 8 cm. H\u1ecfi thanh n\u1eb9p c\u00f2n l\u1ea1i Nam ph\u1ea3i l\u00e0m c\u00f3 \u0111\u1ed9 d\u00e0i bao nhi\u00eau? (Gi\u1ea3 s\u1eed c\u00e1c m\u1ed1i n\u1ed1i kh\u00f4ng \u0111\u00e1ng k\u1ec3.) H\u00ecnh 6 b) M\u1ed9t khung g\u1ed7 ABCD (H\u00ecnh 6) \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh t\u1eeb 5 thanh n\u1eb9p c\u00f3 \u0111\u1ed9 d\u00e0i nh\u01b0 sau: AB = CD = 36 cm; BC = AD = 48 cm; AC = 60 cm. Ch\u1ee9ng minh r\u0103\u0300ng A\uf0b7BC v\u00e0 A\uf0b7DC la\u0300 ca\u0301c go\u0301c vu\u00f4ng.\t \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng 2: HS c\u00f3 c\u01a1 h\u1ed9i v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c v\u1eeba h\u1ecdc v\u00e0o th\u1ef1c t\u1ebf, \u00e1p d\u1ee5ng ki\u1ebfn th\u1ee9c li\u00ean m\u00f4n v\u1eadn d\u1ee5ng t\u1ed5ng h\u1ee3p c\u00e1c k\u0129 n\u0103ng th\u00f4ng qua vi\u1ec7c l\u00e0m m\u1ed9t c\u00e1i \u00eake v\u00e0 ch\u1ee9ng minh m\u1ed9t tam gi\u00e1c vu\u00f4ng d\u1ef1a tr\u00ean s\u1ed1 \u0111o c\u1ee7a ba c\u1ea1nh. \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c V\u1eadn d\u1ee5ng 2: HS tra\u0309 l\u01a1\u0300i y\u00eau c\u1ea7u v\u00e0o v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. GV c\u00f3 th\u1ec3 t\u1ed5 ch\u1ee9c cho HS l\u00e0m vi\u1ec7c nh\u00f3m ho\u1eb7c thuy\u1ebft tr\u00ecnh. 85","H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: a) 10 cm; b) Ta c\u00f3 AC2 = AB2 + BC2 = AD2 + CD2, suy ra A\uf0b7BC v\u00e0 A\uf0b7DC l\u00e0 c\u00e1c g\u00f3c vu\u00f4ng. 3. V\u1eadn d\u1ee5ng \u0111\u1ecbnh l\u00ed Pythagore V\u00ed d\u1ee5 3. T\u00ednh kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111i\u1ec3m A, B trong H\u00ecnh 7. B ? A 32 m 41 m 12 m H\u00ecnh 7 Mu\u0323c \u0111i\u0301ch c\u1ee7a V\u00ed d\u1ee5 3: H\u01b0\u01a1\u0301ng d\u00e2\u0303n HS v\u1eadn d\u1ee5ng \u0111\u1ecbnh l\u00ed Pythagore \u0111\u1ec3 t\u00ednh kho\u1ea3ng c\u00e1ch th\u00f4ng qua vi\u1ec7c t\u1ea1o l\u1eadp c\u00e1c tam gi\u00e1c vu\u00f4ng. Th\u1ef1c h\u00e0nh 3. T\u00ednh c\u00e1c \u0111\u1ed9 d\u00e0i PN v\u00e0 BC trong H\u00ecnh 9. O D 7 cm C 4 cm ? 25 cm 30 cm A M 7 cm P ? N H\u00ecnh 9 10 cm B a) b) Mu\u0323c \u0111i\u0301ch c\u1ee7a Th\u1ef1c h\u00e0nh 3: HS th\u01b0\u0323c ha\u0300nh s\u01b0\u0309 du\u0323ng \u0111\u1ecbnh l\u00ed Pythagore trong vi\u1ec7c t\u00ednh c\u00e1c \u0111\u1ed9 d\u00e0i c\u1ea1nh c\u1ee7a tam gi\u00e1c v\u00e0 h\u00ecnh thang vu\u00f4ng \u0111\u00ea\u0309 re\u0300n luy\u00ea\u0323n ki\u0303 n\u0103ng theo y\u00eau c\u00e2\u0300u c\u00e2\u0300n \u0111a\u0323t. V\u1eadn d\u1ee5ng 3. T\u00ednh chi\u1ec1u d\u00e0i c\u1ea7n c\u1ea9u AB A trong H\u00ecnh 10. 5m C 4m B 2m E D H\u00ecnh 10 86","\u2013 Mu\u0323c \u0111i\u0301ch c\u1ee7a V\u1eadn d\u1ee5ng 3: HS c\u00f3 c\u01a1 h\u1ed9i v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c v\u1eeba h\u1ecdc v\u00e0o th\u1ef1c t\u1ebf, \u00e1p d\u1ee5ng ki\u1ebfn th\u1ee9c li\u00ean m\u00f4n, v\u1eadn d\u1ee5ng t\u1ed5ng h\u1ee3p c\u00e1c k\u0129 n\u0103ng th\u00f4ng qua vi\u1ec7c t\u00ednh chi\u1ec1u d\u00e0i c\u1ee7a c\u1ea7n c\u1ea9u. \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c V\u1eadn d\u1ee5ng 3: HS tra\u0309 l\u01a1\u0300i y\u00eau c\u1ea7u v\u00e0o v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: AB = 5 m. IV. H\u01b0\u1edbng d\u1eabn gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp 1. \ta) BC = 25 cm; b) AB = 3 cm; c) AC = 20 cm. 2. \t\u0110\u1ed9 cao c\u1ee7a con di\u1ec1u so v\u1edbi m\u1eb7t \u0111\u1ea5t l\u00e0: 502 \u2212 252 + 1 \u2248 44,3 (m). 3. \ta = 2, b = 3, c = 2, d = 5 . D\u1ef1 \u0111o\u00e1n e = 6, f = 7, g = 8, h = 3, i = 10, j = 11, k = 12, l = 13, m = 14. 4. \ta) Ta c\u00f3 AB2 + AC2 = BC2, suy ra tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i A; b) Ta c\u00f3 AC2 + BC2 = AB2, suy ra tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i C; c) Ta c\u00f3 AB2 + BC2 = AC2, suy ra tam gi\u00e1c ABC vu\u00f4ng t\u1ea1i B. 5. \tChi\u1ec1u cao m\u00e0 thang c\u00f3 th\u1ec3 v\u01b0\u01a1n t\u1edbi l\u00e0 3 + 132 \u2212 52 = 15 (m). 6. \tKho\u1ea3ng c\u00e1ch t\u1eeb thuy\u1ec1n \u0111\u1ebfn \u0111\u1ec9nh th\u00e1p h\u1ea3i \u0111\u0103ng l\u00e0 1802 + 252 \u2248 182 (m). B\u00e0i 2. T\u1ee8 GI\u00c1C I. M\u1ee5c ti\u00eau 1. Y\u00eau c\u1ea7u c\u00e2\u0300n \u0111a\u0323t: \u2013 M\u00f4 t\u1ea3 \u0111\u01b0\u1ee3c t\u1ee9 gi\u00e1c, t\u1ee9 gi\u00e1c l\u1ed3i. \u2013 Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c \u0111\u1ecbnh l\u00ed v\u1ec1 t\u1ed5ng c\u00e1c g\u00f3c c\u1ee7a m\u1ed9t t\u1ee9 gi\u00e1c l\u1ed3i b\u1eb1ng 360o. 2. N\u0103ng l\u1ef1c ch\u00fa tr\u1ecdng: t\u01b0 duy v\u00e0 l\u1eadp lu\u1eadn to\u00e1n h\u1ecdc, m\u00f4 h\u00ecnh ho\u00e1 to\u00e1n h\u1ecdc, giao ti\u00ea\u0301p toa\u0301n ho\u0323c. 3. T\u00edch h\u1ee3p: To\u00e1n h\u1ecdc v\u00e0 cu\u1ed9c s\u1ed1ng, t\u00edch h\u1ee3p c\u00e1c m\u00f4n h\u1ecdc kh\u00e1c. II. M\u1ed9t s\u1ed1 ch\u00fa \u00fd 1. Y\u00eau c\u1ea7u HS m\u00f4 t\u1ea3 ch\u00ednh x\u00e1c t\u1ee9 gi\u00e1c v\u00e0 c\u00e1c kh\u00e1i ni\u1ec7m li\u00ean quan. 2. C\u1ea7n h\u01b0\u1edbng d\u1eabn \u0111\u1ec3 HS gi\u1ea3i th\u00edch t\u00ednh ch\u1ea5t t\u1ed5ng c\u00e1c g\u00f3c trong m\u1ed9t t\u1ee9 gi\u00e1c th\u00f4ng qua t\u00ednh ch\u1ea5t t\u1ed5ng c\u00e1c g\u00f3c c\u1ee7a m\u1ed9t tam gi\u00e1c. 3. Ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n 8 ch\u1ec9 tr\u00ecnh b\u00e0y v\u1ec1 t\u1ee9 gi\u00e1c l\u1ed3i. 87","III. G\u1ee3i \u00fd c\u00e1c ho\u1ea1t \u0111\u1ed9ng c\u1ee5 th\u1ec3 H\u0110K\u0110 H\u00ecnh m\u00e0u xanh b\u00ean \u0111\u01b0\u01a1\u0323c C (Ch\u00e2u \u0110\u00f4\u0301c) L tri\u0301ch ra t\u01b0\u0300 b\u1ea3n \u0111\u1ed3 \u0111\u01b0\u1ee3c (Long Xuy\u00ean) g\u1ecdi l\u00e0 T\u1ee9 gi\u00e1c Long Xuy\u00ean. R (Ra\u0323ch Gia\u0301) Em h\u00e3y cho bi\u1ebft: H \u2013 H\u00ecnh n\u00e0y \u0111\u01b0\u1ee3c t\u1ea1o b\u1edfi (Ha\u0300 Ti\u00ean) m\u1ea5y \u0111o\u1ea1n th\u1eb3ng? \u2013 C\u00e1c \u0111o\u1ea1n th\u1eb3ng n\u00e0y n\u1ed1i c\u00e1c \u0111\u1ecba \u0111i\u1ec3m n\u00e0o? \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a H\u0110K\u0110: HS co\u0301 c\u01a1 h\u00f4\u0323i tr\u1ea3i nghi\u1ec7m, tha\u0309o lu\u00e2\u0323n v\u1ec1 kh\u00e1i ni\u1ec7m t\u1ee9 gi\u00e1c th\u00f4ng qua quan s\u00e1t \u201cT\u1ee9 gi\u00e1c Long Xuy\u00ean\u201d. C\u00e1ch \u0111\u1eb7t v\u1ea5n \u0111\u1ec1 n\u00e0y c\u00f3 kh\u1ea3 n\u0103ng thu h\u00fat HS v\u00e0o b\u00e0i h\u1ecdc. \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c H\u0110K\u0110: GV n\u00eau c\u00e2u h\u1ecfi, HS tra\u0309 l\u01a1\u0300i, l\u01a1\u0301p nh\u1eadn x\u00e9t, GV s\u1eed d\u1ee5ng c\u01a1 h\u1ed9i \u0111\u1ec3 gi\u1edbi thi\u1ec7u b\u00e0i. L\u01b0u \u00fd: GV c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng Google Maps \u0111\u1ec3 t\u1ea1o ra c\u00e1c t\u1ee9 gi\u00e1c li\u00ean quan \u0111\u1ebfn c\u00e1c \u0111\u1ecba \u0111i\u1ec3m g\u1ea7n v\u1edbi \u0111\u1ecba b\u00e0n c\u1ee7a tr\u01b0\u1eddng \u0111\u1ec3 t\u0103ng t\u00ednh th\u1ef1c t\u1ebf cho b\u00e0i d\u1ea1y. 1. T\u1ee9 gi\u00e1c H\u0110KP 1, 2 T\u1ee9 Tg\u1ee9i\u00e1gcil\u00e1\u1ed3ci l\u1ed3i 2 V\u1ebd c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng l\u00e2\u0300n l\u01b0\u01a1\u0323t ch\u1ee9a m\u1ed7i c\u1ea1nh c\u1ee7a c\u00e1c t\u1ee9 gi\u00e1c sau \u0111\u00e2y v\u00e0 n\u00eau nh\u1eadn x\u00e9t c\u1ee7a em v\u1ec1 v\u1ecb tr\u00ed c\u1ee7a m\u1ed7i t\u1ee9 gi\u00e1c \u0111\u1ed1i v\u1edbi m\u1ed7i \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00e3 v\u1ebd. B B B A A CA C b) D D C D a) c) H\u00ecnh 2 88 T\u1ee9 gi\u00e1c l\u1ed3i l\u00e0 t\u1ee9 gi\u00e1c lu\u00f4n n\u1eb1m trong cu\u0300ng m\u1ed9t ph\u00e2\u0300n m\u1eb7t ph\u1eb3ng \u0111\u01b0\u01a1\u0323c ph\u00e2n chia b\u01a1\u0309i","\u2013 M\u1ee5c \u0111\u00edch cu\u0309a H\u0110KP 1, 2: Gi\u00fap HS co\u0301 c\u01a1 h\u00f4\u0323i tr\u1ea3i nghi\u1ec7m, tha\u0309o lu\u00e2\u0323n v\u1ec1 kh\u00e1i ni\u1ec7m t\u1ee9 gi\u00e1c v\u00e0 t\u1ee9 gi\u00e1c l\u1ed3i. \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c H\u0110KP 1, 2: GV n\u00eau c\u00e2u h\u1ecfi, HS tra\u0309 l\u01a1\u0300i, l\u01a1\u0301p nh\u1eadn x\u00e9t, GV \u0111a\u0301nh gia\u0301. Th\u1ef1c h\u00e0nh 1. V\u1ebd t\u1ee9 gi\u00e1c MNPQ v\u00e0 t\u00ecm: \u2013 Hai \u0111\u1ec9nh \u0111\u1ed1i nhau; \u2013 Hai \u0111\u01b0\u1eddng ch\u00e9o; \u2013 Hai c\u1ea1nh \u0111\u1ed1i nhau. M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 1: HS th\u01b0\u0323c ha\u0300nh nh\u1eadn d\u1ea1ng c\u00e1c y\u1ebfu t\u1ed1 c\u1ee7a m\u1ed9t t\u1ee9 gi\u00e1c l\u1ed3i \u0111\u1ec3 r\u00e8n luy\u1ec7n k\u0129 n\u0103ng theo y\u00eau c\u1ea7u c\u1ea7n \u0111\u1ea1t. V\u1eadn d\u1ee5ng 1. T\u00ecm c\u00e1c \u0111\u1ec9nh, c\u1ea1nh v\u00e0 \u0111\u01b0\u1eddng ch\u00e9o C (Ch\u00e2u \u0110\u00f4\u0301c) c\u1ee7a t\u1ee9 gi\u00e1c Long Xuy\u00ean CHRL (H\u00ecnh 6). \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng 1: HS c\u00f3 c\u01a1 h\u1ed9i v\u1eadn H L d\u1ee5ng ki\u1ebfn th\u1ee9c v\u1ec1 t\u1ee9 gi\u00e1c v\u1eeba h\u1ecdc v\u00e0o th\u1ef1c t\u1ebf. (Ha\u0300 Ti\u00ean) (Long Xuy\u00ean) \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c V\u1eadn d\u1ee5ng 1: HS tra\u0309 l\u01a1\u0300i y\u00eau c\u1ea7u R (Ra\u0323ch Gia\u0301) v\u00e0o v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. GV c\u00f3 th\u1ec3 s\u1eed H\u00ecnh 6 d\u1ee5ng Google Maps \u0111\u1ec3 t\u1ea1o ra c\u00e1c t\u1ee9 gi\u00e1c li\u00ean quan \u0111\u1ebfn c\u00e1c \u0111\u1ecba \u0111i\u1ec3m g\u1ea7n v\u1edbi khu v\u1ef1c c\u1ee7a tr\u01b0\u1eddng \u0111\u1ec3 t\u0103ng t\u00ednh th\u1ef1c t\u1ebf cho b\u00e0i d\u1ea1y. 2. T\u1ed5ng c\u00e1c g\u00f3c c\u1ee7a m\u1ed9t t\u1ee9 gi\u00e1c H\u0110KP 3 \u2013 Mu\u0323c \u0111i\u0301ch cu\u0309a H\u0110KP 3: HS l\u00e0m quen v\u1edbi c\u00e1ch t\u00ednh t\u1ed5ng c\u00e1c g\u00f3c trong m\u1ed9t t\u1ee9 gi\u00e1c qua vi\u1ec7c ph\u00e2n chia t\u1ee9 gi\u00e1c th\u00e0nh hai tam gi\u00e1c. \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c H\u0110KP 3: GV n\u00eau c\u00e2u h\u1ecfi, HS tra\u0309 l\u01a1\u0300i, l\u01a1\u0301p nh\u1eadn x\u00e9t, GV \u0111a\u0301nh gia\u0301. Th\u1ef1c h\u00e0nh 2. T\u00ecm x trong m\u1ed7i t\u1ee9 gi\u00e1c sau: P D xA E F 80o 99o 70o S x 2x C 100o 95o x G Q R B H a) b) c) H\u00ecnh 9 89","\u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 2: HS th\u01b0\u0323c ha\u0300nh t\u00ecm s\u1ed1 \u0111o g\u00f3c ch\u01b0a bi\u1ebft c\u1ee7a m\u1ed9t t\u1ee9 gi\u00e1c \u0111\u1ec3 r\u00e8n luy\u1ec7n k\u0129 n\u0103ng theo y\u00eau c\u1ea7u c\u1ea7n \u0111\u1ea1t. \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c Th\u1ef1c h\u00e0nh 2: HS tra\u0309 l\u01a1\u0300i y\u00eau c\u1ea7u v\u00e0o v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. V\u1eadn d\u1ee5ng 2. Ph\u1ea7n th\u00e2n c\u1ee7a c\u00e1i di\u1ec1u A D \u1edf H\u00ecnh 10a \u0111\u01b0\u1ee3c v\u1ebd l\u1ea1i nh\u01b0 H\u00ecnh 10b. B 130o T\u00ecm s\u1ed1 \u0111o c\u00e1c g\u00f3c ch\u01b0a bi\u1ebft trong h\u00ecnh. a) 60o \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng 2: HS c\u00f3 c\u01a1 h\u1ed9i H\u00ecnh 10 v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c v\u1eeba h\u1ecdc v\u00e0o th\u1ef1c t\u1ebf C t\u00ecm s\u1ed1 \u0111o g\u00f3c ch\u01b0a bi\u1ebft tr\u00ean h\u00ecnh con di\u1ec1u. b) \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c V\u1eadn d\u1ee5ng 2: HS tra\u0309 l\u01a1\u0300i y\u00eau c\u1ea7u v\u00e0o v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. GV c\u00f3 th\u1ec3 t\u00ecm th\u00eam c\u00e1c h\u00ecnh quen thu\u1ed9c kh\u00e1c \u0111\u1ec3 t\u0103ng t\u00ednh s\u00e1ng t\u1ea1o cho b\u00e0i d\u1ea1y. C\u00f3 th\u1ec3 t\u1ed5 ch\u1ee9c cho HS l\u00e0m vi\u1ec7c nh\u00f3m ho\u1eb7c thuy\u1ebft tr\u00ecnh. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: A\uf0b7BC = A\uf0b7DC = 85o. IV. H\u01b0\u1edbng d\u1eabn gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp 1. a) B\uf0b5 = 360o \u2013 (110o + 75o + 75o) = 100o; b) M\uf0b5 = 360o \u2013 (70o + 90o + 90o) = 110o; c) T\uf0b7SV = 180o \u2013 60o = 120o, V\uf0b5 = 360o \u2013 (65o + 120o + 115o) = 60o; d) F\uf024 = 360o \u2013 (80o + 100o + 70o) = 110o. 2. A\uf0b51 + B\uf0b51 + C\uf0b51 + D\uf0b5 1 = 4 . 180o \u2013 (A\uf0b5 + B\uf0b5 + C\uf0b5 + D\uf0b5 ) = 4 . 180o \u2013 360o = 360o. 3. Ta c\u00f3 B\uf0b5 = 180o \u2013 110o = 70o, suy ra D\uf0b5 = 360o \u2013 (100o + 75o + 70o) = 115o. 4. Ta c\u00f3 A\uf0b5 = 180o \u2013 65o = 115o, B\uf0b5 = 180o \u2013 100o = 80o, C\uf0b5 = 180o \u2013 60o = 120o, D\uf0b5 = 360o \u2013 (115o + 80o + 120o) = 45o. Suy ra g\u00f3c ngo\u00e0i t\u1ea1i \u0111\u1ec9nh D b\u1eb1ng 180o \u2013 45o = 135o. 5. Ta c\u00f3 x + 2x + 3x + 4x = 360o, suy ra x = 36o. Suy ra A\uf0b5 = 36o, B\uf0b5 = 72o, C\uf0b5 = 108o, D\uf0b5 = 144o. 6. \ta) Ta c\u00f3 hai \u0111i\u1ec3m A v\u00e0 C c\u00e1ch \u0111\u1ec1u hai \u0111\u1ea7u m\u00fat c\u1ee7a \u0111o\u1ea1n th\u1eb3ng BD, suy ra A v\u00e0 C n\u1eb1m tr\u00ean trung tr\u1ef1c c\u1ee7a BD, suy ra AC l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a BD. b) Ta c\u00f3 \u0394ABC = \u0394ADC (c.c.c), suy ra D\uf0b5 = B\uf0b5 = 95o, A\uf0b5 = 360o \u2013 (95o + 95o + 35o) = 135o. 7. a) Hai c\u1ea1nh k\u1ec1 v\u1edbi c\u1ea1nh BD l\u00e0 BQ v\u00e0 DN. C\u1ea1nh \u0111\u1ed1i c\u1ee7a c\u1ea1nh BD l\u00e0 NQ; b) BN v\u00e0 DQ l\u00e0 hai \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a t\u1ee9 gi\u00e1c BDNQ. 90","B\u00e0i 3. H\u00ccNH THANG \u2013 H\u00ccNH THANG C\u00c2N I. M\u1ee5c ti\u00eau 1. Y\u00eau c\u1ea7u c\u00e2\u0300n \u0111a\u0323t: \u2013 Nh\u1eadn bi\u1ebft \u0111\u01b0\u1ee3c h\u00ecnh thang, h\u00ecnh thang c\u00e2n, h\u00ecnh thang vu\u00f4ng. \u2013 Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c t\u00ednh ch\u1ea5t v\u1ec1 g\u00f3c k\u1ec1 m\u1ed9t \u0111\u00e1y, c\u1ea1nh b\u00ean, \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh thang c\u00e2n. \u2013 Nh\u1eadn bi\u1ebft \u0111\u01b0\u1ee3c d\u1ea5u hi\u1ec7u \u0111\u1ec3 m\u1ed9t h\u00ecnh thang l\u00e0 h\u00ecnh thang c\u00e2n (v\u00ed d\u1ee5: h\u00ecnh thang c\u00f3 hai \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng nhau l\u00e0 h\u00ecnh thang c\u00e2n). 2. N\u0103ng l\u1ef1c ch\u00fa tr\u1ecdng: t\u01b0 duy v\u00e0 l\u1eadp lu\u1eadn to\u00e1n h\u1ecdc, m\u00f4 h\u00ecnh ho\u00e1 to\u00e1n h\u1ecdc, giao ti\u00ea\u0301p toa\u0301n ho\u0323c. 3. T\u00edch h\u1ee3p: To\u00e1n h\u1ecdc v\u00e0 cu\u1ed9c s\u1ed1ng, t\u00edch h\u1ee3p c\u00e1c m\u00f4n h\u1ecdc kh\u00e1c. II. M\u1ed9t s\u1ed1 ch\u00fa \u00fd 1. GV s\u1eed d\u1ee5ng c\u00e1c h\u00ecnh \u1ea3nh quen thu\u1ed9c trong th\u1ef1c t\u1ebf \u0111\u1ec3 gi\u00fap HS nh\u1eadn bi\u1ebft h\u00ecnh thang, h\u00ecnh thang c\u00e2n. 2. GV c\u1ea7n \u00f4n t\u1eadp v\u00e0 c\u1ee7ng c\u1ed1 c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 c\u1eb7p g\u00f3c so le trong v\u00e0 c\u1eb7p g\u00f3c \u0111\u1ed3ng v\u1ecb \u0111\u1ec3 gi\u00fap HS kh\u00e1m ph\u00e1 c\u00e1c t\u00ednh ch\u1ea5t c\u1ee7a h\u00ecnh thang c\u00e2n. 3. C\u1ea7n l\u01b0u \u00fd nh\u1eafc nh\u1edf HS: H\u00ecnh thang c\u00e2n l\u00e0 h\u00ecnh c\u00f3 hai c\u1ea1nh b\u00ean b\u1eb1ng nhau, nh\u01b0ng h\u00ecnh thang c\u00f3 hai c\u1ea1nh b\u00ean b\u1eb1ng nhau ch\u01b0a ch\u1eafc \u0111\u00e3 l\u00e0 h\u00ecnh thang c\u00e2n. III. G\u1ee3i \u00fd c\u00e1c ho\u1ea1t \u0111\u1ed9ng c\u1ee5 th\u1ec3 H\u0110K\u0110 M\u00e1i ng\u00f3i c\u1ee7a tr\u1ee5 s\u1edf U\u1ef7 ban AB nh\u00e2n d\u00e2n Th\u00e0nh ph\u1ed1 H\u1ed3 Ch\u00ed Minh DC c\u00f3 h\u00ecnh d\u1ea1ng m\u1ed9t t\u1ee9 gi\u00e1c ABCD. N\u00eau nh\u1eadn x\u00e9t c\u1ee7a em v\u1ec1 hai c\u1ea1nh AB v\u00e0 CD c\u1ee7a t\u1ee9 gi\u00e1c n\u00e0y. \u2013 M\u1ee5c \u0111\u00edch cu\u0309a H\u0110K\u0110: Gi\u00fap HS co\u0301 c\u01a1 h\u00f4\u0323i tr\u1ea3i nghi\u1ec7m, tha\u0309o lu\u00e2\u0323n v\u1ec1 vi\u1ec7c nh\u1eadn bi\u1ebft c\u00e1c h\u00ecnh thang trong th\u1ef1c t\u1ebf. C\u00e1ch \u0111\u1eb7t v\u1ea5n \u0111\u1ec1 n\u00e0y c\u00f3 kh\u1ea3 n\u0103ng thu h\u00fat HS v\u00e0o b\u00e0i h\u1ecdc. \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c H\u0110K\u0110: GV n\u00eau c\u00e2u h\u1ecfi, HS tra\u0309 l\u01a1\u0300i, l\u01a1\u0301p nh\u1eadn x\u00e9t, GV s\u1eed d\u1ee5ng c\u01a1 h\u1ed9i \u0111\u1ec3 gi\u1edbi thi\u1ec7u b\u00e0i. L\u01b0u \u00fd: GV c\u00f3 th\u1ec3 t\u00ecm ki\u1ebfm c\u00e1c h\u00ecnh \u1ea3nh s\u00e1ng t\u1ea1o h\u01a1n c\u00f3 li\u00ean quan \u0111\u1ebfn \u0111\u1ecba ph\u01b0\u01a1ng, tr\u01b0\u1eddng h\u1ecdc \u0111\u1ec3 t\u1ea1o s\u1ef1 ch\u00fa \u00fd v\u00e0 th\u00edch th\u00fa cho HS. 91","c\u00f3 h\u00ecnh d\u1ea1ng m\u1ed9t t\u1ee9 gi\u00e1c ABCD. AB N\u00eau nh\u1eadn x\u00e9t c\u1ee7a em v\u1ec1 hai DC c\u1ea1nh AB v\u00e0 CD c\u1ee7a t\u1ee9 gi\u00e1c n\u00e0y. 1. H\u00ecnh thang \u2013 H\u00ecnh thang c\u00e2n AB 1H.\u0110HK\u00ccPN1H THANG \u2013 H\u00ccNH THANG C\u00c2N 1 T\u1ee9 gi\u00e1c ABCD (H\u00ecnh 1b) l\u00e0 h\u00ecnh v\u1ebd minh ho\u1ea1 m\u1ed9t ph\u1ea7n c\u1ee7a chi\u1ebfc thang \u1edf H\u00ecnh 1a. N\u00eau nh\u1eadn x\u00e9t c\u1ee7a em v\u1ec1 hai c\u1ea1nh AB v\u00e0 CD c\u1ee7a t\u1ee9 gi\u00e1c n\u00e0y. V\u00ed d\u1ee5 1. T\u00ecm c\u00e1c g\u00f3c ch\u01b0aDbi\u1ebft c\u1ee7a h\u00ecnhCthang ABCD tr\u01b0\u1eddng h\u1ee3p sau: a) A\uf0b5 = 90o v\u00e0 B\uf0b5 = 40o.; b) C\uf0b5= D\uf0b5= 8a0)o. H\u00ecnh 1 b) \u2013 MH\u1ee5\u00eccnh\u0111\u00edtchhancgu\u0309al\u00e0Ht\u1ee9\u0110gKi\u00e1Pc 1c\u00f3: Ghai\u00fai pc\u1ea1HnhS\u0111c\u1ed1o\u0301i sco\u01a1nhg\u00f4\u0323siotnar)g\u1ea3.Hi n\u00ecnghhit\u1ec7hman,gthAaB\u0309oCluD\u00e2\u0323(nAvB\u1ec1 \/n\/ hC\u1eadDn)bci\u00f3\u1ebftA\uf0b5h\u00ec=nhG90i\u1ea3o in\u00ean l\u00e0 h\u00ecnh tha\u2013ngGtH\u01a1h\u0323i\u00ec\u00f4nynh\u0301gt2\u00f4\u0309qlcu\u00e0hah\u01b0v\u0301\u00eccnih\u1ec7Hcth\u0110qauKnagPnA1sB:\u00e1tGCmDV\u1ed9vnt\u1edb\u00eapiuhA\u1ea7cBn\u00e2uc\/\/\u1ee7hCa\u1ecfDic,h.HiT\u1ebfSacb\u00c1ct)tpr\u00f3hHa:\u0309ad\u00ecln\u1ee5n\u01a1\u0300gnhi.,gtlh\u0111\u01a1\u0301a\u1ecbpnnhnghlA\u00ed\u1eadBnt\u1ed5ACxn\u00e9gDt\u0111,c(\u00e1\u00e1GAycnVBhg\u1ecf\u00f3\u0111\/\/ca\u0301CnBcDh\u1ee7a)gmica\u00f3\u0301\u1ed9. tC\uf0b5=t\u1ee9 ta c\u00f3 C\uf0b5 c\u1ea1nh b\u00ean gi\u00e1c, 80o n\u00ean \u0111\u01b0\u1eddng cao D\uf0b5= Th\u1ef1\u2013cCh\u00e1\u00e0cn\u0111ho\u1ea11n.tTh\u1eb3\u00ecmngcA\u00e1Bc,gC\u00f3Dc gch\u1ecdi\u01b0la\u00e0 bc\u00e1i\u1ebfctcc\u1ea1\u1ee7nah h\u0111\u00e1\u00ecnyh(Shtuhoy\u1eb7acnrag\u0111\u00e1AM\uf0b5y)N.=PB\uf0b5Q=c1\u00f380hao i\u2212\u01118\u00e10yol\u00e0=M10N0ov. \u00e0 QP c\u1ea1nh b\u00ean tronNg\u1ebfmu A\u1ed7iBtr<\u01b0\u1eddCnDg thh\u1ee3\u00ec Ap Bsalu\u00e0 v\u0111\u00e0\u00e1yn\u00eanuh\u1ecfn,hC\u1eadDn xl\u00e0\u00e9t\u0111\u00e1cy\u1ee7alT\u1edbenhm.\u1ef1.c h\u00e0nh 1. T\u00ecm c\u00e1c g\u00f3c ch\u01b0a bi\u1ebft c\u1ee7a h\u00ecnh thang baM))\u1ee5QP\uf0b5\uf024=\u2013\u2013\u0111coAC\u0111=\u1ea1\u00ed\u00e1HnQ\uf0b5c9=ch0tlh\u0111o\u00e0c\u1eb3o1\u1ee7\u0111nv\u1ea11a\u01b0g\u00e0n0\u1eddTAtoN\uf0b5nh.hHg\u1eb3\u1ef1=nvgcg1u\u1ecdh2A\u00f4i\u00e05nlDn\u00e0og.;h,\u0111gB\u01b01\u00f3C\u1edd:cnHklg\u00e0\u1ebbScctta\u00e1\u1eebhco\u01b0A\u0323ccc\u1ea1\u1ee7\u0111hna\u1ebfhan\u0300hnb\u00ec\u0111hn\u00ea\u01b0hnt\u1edd\u00ed.tnnhghabtantrs))hgo\u1ed1\u1eb3.QnP\uf0b5\uf024=n\u0111ggo=mCgQ\uf0b59=\u1ed7\u00f3D0ico,t1rcv\u01b0h1\u00e0\u1eddD\u01b00naoN\uf0b5.gb=hiH\u1ebf\u1ee31tp2c5s\u1ee7oaa.;uH\u0111m\u00e1v\u00ecyn\u1ed9\u00e0hl\u1edbtn2nh\u00ea\u00ecunhnhth\u1eadnanxg\u00e9Ct c\u1ee7a em. Vr\u00e8\u1eadnnHlud\u00ecny\u1ee5h\u1ec7nntghka1\u0129n.ngM\u0103cn\u00e2\u1ed9gnt tmlh\u00e0e\u1eb7hot\u00ectny\u01b0h\u00ea\u1eddutnhgca\u1ea7ncug\u1ee7cac\u00f3\u1ea7cnha\u00e2\u0111in\u1ea1gtt.\u00f3hc\u00e1pk\u1ec1c\u1ed9mt(V\u1ed9Hc\u1eadt\u1edd\u00ecn\u0111n\u00e1hdy\u1ee54bn)\u1eb1.gnCg1hn.ohMbau\u1ed9i\u1ebf.ttmD\uf0b5=\u1eb7t \u0111\u1ec3 t\u01b0\u1eddng c\u1ee7a Tch\u00ecm\u00e2nst\u1ed1h\u00e1\u0111pocA\u1ed9\uf0b5t c\u1edd HB\uf0b5\u00e0. N C\uf0b5= 75o. v\u00e0 H\u00e0 N\u1ed9i c\u00f3 d\u1ea1ng h\u00ecnh thang c\u00e2n ABCD (H\u00ecnh 4). B Q P C\u2013 hMoH\u0111A\uf0b5\u1ee5\u00e1b\u00eccyn=i\u1ebfhl\u0111tB\uf0b5\u00e0t\u00edDh\uf0b5Ac;=ahBC\uf0b5ngcv=C\uf0b5\u1ee7=c\u00e0aD\uf0b5\u00e2Cn.VD7A\u1ead5B(noH.Cd\u00ecTDn\u1ee5\u00echmnvg3\u1edbasi1\u1ed1)h:c\u0111a\u00f3Hio SA\uf0b5c\u00f3vA\u00e0cB\u01a1\uf0b5.h\u1ed9i v\u1eadn d\u1ee5ng kHi\u1ebf\u00ecnnhtthh\u1ee9ancgvc\u1eeb\u00f3amh\u1ed9\u1ecdtcg\u00f3vc\u00e0ovut\u00f4hn\u1ef1gc t\u1ebf t\u00ednh g\u00f3c c\u1ee7a AB m\u1ed9t m\u0111\u1eb7\u01b0t \u01a1t\u0323\u01b0c\u1eddgn\u1ecdgi lt\u00e0\u1ea1ihc\u00ecnhh\u00e2nthtahn\u00e1gpvcu\u1ed9\u00f4tncg\u1edd HD\u00e0 N\u1ed9i c\u00f3 d\u1ea1an)g CM b) N h\u00ecnh th(Han\u00ecngh. 3b). H\u00ecnh 3 D C 68\u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c V\u1eadn d\u1ee5ng 1: HS tra\u0309 lt\u01a1h\u0300i\u1ec3yt\u1ed5\u00eauchcV\u1ee9\u1ea7\u1eaducn d\u1ee5ng 2. T\u1ee9 gi\u00e1c H\u00ecnh 4 c\u00f3 c\u00e1c g\u00f3c cho nh\u01b0 tron v\u00e0o v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. GV c\u00f3 EFGH cho HS l\u00e0m vi\u1ec7c nh\u00f3m ho\u1eb7c thuy\u1ebft tr\u00ecnh. cho a) Ch\u1ee9ng minh r\u1eb1ng EFGH lg\u00e0i\u00e18hc5\u00ecn.o hFthang. V\u1eadn d\u1ee5ng 2. T\u1ee9 gi\u00e1c EFGH c\u00f3 c\u00e1c g\u00f3c nhb\u01b0)tTro\u00ecmnggH\u00f3\u00eccnchh5\u01b0.a bi\u1ebft cE\u1ee7a9t5\u1ee9o a) Ch\u1ee9ng minh r\u1eb1ng EFGH l\u00e0 h\u00ecnh thang. 2. T\u00cdNH CH\u1ea4T C\u1ee6A HH\u00ccNH THANG C\u00c2N b) T\u00ecm g\u00f3c ch\u01b0a bi\u1ebft c\u1ee7a t\u1ee9 gi\u00e1c. 2 a) Cho h\u00ecnh thang c\u00e2n ABCD c\u00f3 hai D \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng 2: HS c\u00f3 c\u01a1 h\u1ed9i v\u1eadn\u0111d\u00e1\u1ee5ynlg\u00e0kAi\u1ebfBnvth\u00e0\u1ee9CcD (AB > CD). Qu2a7oC v\u1eeba h\u1ecdc v\u00e0o th\u1ef1c t\u1ebf ch\u1ee9ng minh m\u1ed9t t\u1ee9 gi\u00e1c l\u00e0 h\u00ecvn\u1ebdh\u0111t\u01b0h\u1eddanngg tthh\u00f4\u1eb3nngg song song v\u1edbi AD v\u00e0 qua s\u1ed1 \u0111o c\u00e1c g\u00f3c. c\u1eaft AB t\u1ea1i E (H\u00ecnh 6a). H\u00ecnh 5 G 92 i)Tam gi\u00e1c CEB l\u00e0 tam gi\u00e1c g\u00ec?V\u00ec sao? A a) ii) So s\u00e1nh AD v\u00e0 BC. b) Cho h\u00ecnh thang c\u00e2n MNPQ c\u00f3 hai \u0111\u00e1y l\u00e0 MN v\u00e0 P","b) P= Q= 110 . V\u1eadn d\u1ee5ng 1. M\u1ed9t m\u1eb7t t\u01b0\u1eddng c\u1ee7a ch\u00e2n th\u00e1p c\u1ed9t c\u1edd H\u00e0 N\u1ed9i c\u00f3 d\u1ea1ng h\u00ecnh thang c\u00e2n ABCD (H\u00ecnh 4). Cho bi\u1ebft D\uf0b5= C\uf0b5= 75o. T\u00ecm s\u1ed1 \u0111o A\uf0b5 v\u00e0 B\uf0b5. E 95o 85o F \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c V\u1eadn d\u1ee5ng 2: HS tra\u0309 l\u01a1\u0300i y\u00eau c\u1ea7u v\u00e0o v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. GV c\u00f3 th\u1ec3 t\u1ed5 ch\u1ee9c cho HS l\u00e0m vi\u1ec7c nh\u00f3m ho\u1eb7c thuy\u1ebft tr\u00ecnh. H H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: A B a) V\u1ebd tia Ex l\u00e0 tia \u0111\u1ed1i c\u1ee7a tia EF. TaCc\u00f3 H\uf0b7Ex = 180o \u2013 95o = 85o = G\uf0b7FE.27o D Suy ra HE \/\/ FG. V\u1eady t\u1ee9Hg\u00ecni\u00e1hc4 EFGH l\u00e0 h\u00ecnh thang. H\u00ecnh 5 G b) E\uf0b7VH\u1eadGn d=\u1ee53n6g0o2\u2013. T(\u1ee995goi\u00e1+c8E5FoG+H2c7\u00f3o)c=\u00e1c1g5\u00f33co.cho nh\u01b0 trong H\u00ecnh 5. a) Ch\u1ee9ng minh r\u1eb1ng EFGH l\u00e0 h\u00ecnh thang. 2. Tb\u00edn) hT\u00eccmh\u1ea5gt\u00f3cc\u1ee7cha\u01b0ha\u00ecnbih\u1ebftthc\u1ee7aantg\u1ee9cg\u00e2i\u00e1nc. 2H.\u0110TK\u00cdPN2H CH\u1ea4T C\u1ee6A H\u00ccNH THANG C\u00c2N 2 a) Cho h\u00ecnh thang c\u00e2n ABCD c\u00f3 hai D CQ P \u0111\u00e1y l\u00e0 AB v\u00e0 CD (AB > CD). Qua C v\u1ebd \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi AD v\u00e0 c\u1eaft AB t\u1ea1i E (H\u00ecnh 6a). i)Tam gi\u00e1c CEB l\u00e0 tam gi\u00e1c g\u00ec?V\u00ec sao? A E BM N ii) So s\u00e1nh AD v\u00e0 BC. a) H\u00ecnh 6 b) b) Cho h\u00ecnh thang c\u00e2n MNPQ c\u00f3 hai \u0111\u00e1y l\u00e0 MN v\u00e0 PQ (H\u00ecnh 6b). So s\u00e1nh MP v\u00e0 NQ. Gi\u1ea3i th\u00edch. \u2013 Mu\u0323c \u0111i\u0301ch cu\u0309a H\u0110KP 2: Gi\u00fap HS l\u00e0m quen v\u1edbi t\u00ednh ch\u1ea5t v\u1ec1 c\u1ea1nh b\u00ean v\u00e0 \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnT\u2013hrHotnahgiacnh\u1ea1g\u00ecnnhch\u00e2btnh\u00eaanqnubga\u1eb1cnv\u00e2gin\u1ec7n:chnauh.\u1eadn bi\u1ebft c\u00e1c tam gi\u00e1c b\u1eb1ng nhau. \u2013 G\u2013\u01a1\u0323iHya\u0301 it\u00f4\u0111\u0309\u01b0c\u1eddhn\u01b0\u0301gccHh\u00e9\u0110oKbP\u1eb1n2g: nGhVaun. \u00eau c\u00e2u h\u1ecfi, HS tra\u0309 l\u01a1\u0300i, l\u01a1\u0301p nh\u1eadn x\u00e9t, GV \u0111a\u0301nh gia\u0301. Th\u1ef1c h\u00e0nh 2. T\u00ecm c\u00e1c \u0111o\u1ea1n th\u1eb3ng b\u1eb1ng nhau trong h\u00ecnh thang c\u00e2n MNPQ c\u00f3 hai \u0111\u00e16y9 l\u00e0 MN v\u00e0 PQ. \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 2: HS th\u01b0\u0323c ha\u0300nh t\u00ecm c\u00e1c \u0111o\u1ea1n th\u1eb3ng b\u1eb1ng nhau trong m\u1ed9t h\u00ecnh thang c\u00e2n \u0111\u1ec3 r\u00e8n luy\u1ec7n k\u0129 n\u0103ng theo y\u00eau c\u1ea7u c\u1ea7n \u0111\u1ea1t. \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c Th\u1ef1c h\u00e0nh 2: HS tra\u0309 l\u01a1\u0300i y\u00eau c\u1ea7u v\u00e0o v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. V\u1eadn d\u1ee5ng 3. M\u1ed9t khung c\u1eeda s\u1ed5 h\u00ecnh 3m C thang c\u00e2n c\u00f3 chi\u1ec1u cao 3 m, hai \u0111\u00e1y l\u00e0 DH 3 m v\u00e0 1 m (H\u00ecnh 9). T\u00ecm \u0111\u1ed9 d\u00e0i hai c\u1ea1nh b\u00ean v\u00e0 hai \u0111\u01b0\u1eddng ch\u00e9o. \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng 3: HS c\u00f3 3m c\u01a1 h\u1ed9i v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c v\u1eeba h\u1ecdc v\u00e0o t\u00ecm \u0111\u1ed9 d\u00e0i c\u1ea1nh b\u00ean v\u00e0 \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a A 1m B h\u00ecnh thang c\u00e2n khi bi\u1ebft \u0111\u1ed9 d\u00e0i hai \u0111\u00e1y v\u00e0 chi\u1ec1u cao. H\u00ecnh 9 \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c V\u1eadn d\u1ee5ng 3: HS tra\u0309 l\u01a1\u0300i y\u00eau c\u1ea7u v\u00e0o v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: AD = BC = 10 m, AC = BD = 13 m. 93","V\u1eadn d\u1ee5ng 3. M\u1ed9t khung c\u1eeda s\u1ed5 h\u00ecnh 3m thang c\u00e2n c\u00f3 chi\u1ec1u cao 3 m, hai \u0111\u00e1y l\u00e0 A 1m B 3 m v\u00e0 1 m (H\u00ecnh 9). T\u00ecm \u0111\u1ed9 d\u00e0i hai c\u1ea1nh b\u00ean v\u00e0 hai \u0111\u01b0\u1eddng ch\u00e9o. H\u00ecnh 9 3. D\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft h\u00ecnh thang c\u00e2n 3H.\u0110DK\u1ea4PU3 HI\u1ec6U NH\u1eacN BI\u1ebeT H\u00ccNH THANG C\u00c2N 3 Cho h\u00ecnh thang ABCD c\u00f3 hai \u0111\u00e1y l\u00e0 AB, CD D C v\u00e0 c\u00f3 hai \u0111\u01b0\u1eddng ch\u00e9o b\u1eb1ng nhau (H\u00ecnh 10). V\u1ebd A \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua C, song song v\u1edbi BD v\u00e0 c\u1eaft B E AB t\u1ea1i E. H\u00ecnh 10 a) Tam gi\u00e1c CAE l\u00e0 tam gi\u00e1c g\u00ec? V\u00ec sao? b) So s\u00e1nh tam gi\u00e1c ABD v\u00e0 tam gi\u00e1c BAC. \u2013 M\u2013u\u0323Hc\u00ecn\u0111hi\u0301cthhacnug\u0309ac\u00f3Hh\u0110aiKgP\u00f3c3k:\u1ec1Hm\u01b0\u1ed9\u01a1t\u0301n\u0111g\u00e1ydb\u00e2\u0303\u1eb1nngHnShalu\u00e0ml\u00e0 hq\u00ecunehnthva\u1edbngi cc\u00e2\u00e1nc. d\u1ea5u hi\u1ec7u nh\u1eadn bi\u1ebft h\u00ecnh th\u2013aHng\u00ecnch\u00e2tnhatnhg\u00f4ncg\u00f3 qhauia\u0111v\u01b0i\u1edd\u1ec7ncgsochs\u00e9\u00e1onhb\u1eb1tnagmnghia\u00e1uc.l\u00e0 h\u00ecnh thang c\u00e2n. \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c H\u0110KP 3: GV y\u00eau c\u00e2\u0300u HS tra\u0309 l\u01a1\u0300i, l\u01a1\u0301p nh\u1eadn x\u00e9t, GV \u0111a\u0301nh gia\u0301. V\u00ed d\u1ee5 3. T\u00ecm h\u00ecnh thang c\u00e2n trong c\u00e1c h\u00ecnh thang sau. Th\u1ef1c h\u00e0nh 3Q. S\u1eed dP\u1ee5ng th\u01b0\u1edbHc \u0111o g\u00f3c v\u00e0 th\u01b0\u1edbc \u0111o G\u0111\u1ed9 d\u00e0i \u0111\u1ec3Dt\u00ecm h\u00ecnh thanCg c\u00e2n trong c\u00e1c t\u1ee9 gi\u00e1c \u1edf H\u00ecnh 12. 5 cm 5 cm S T 5 cm 7 cm A B 62o 62o M N E FA B PQ \/\/ MN a) D a) CH\u00ecnbh) 11 V b) U c) 70 F GM N O E c) H Q P d) H\u00ecnh 12 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 3: HS th\u01b0\u0323c ha\u0300nh nh\u1eadn bi\u1ebft m\u1ed9t t\u1ee9 gi\u00e1c l\u00e0 h\u00ecnh thang c\u00e2n \u0111\u00ea\u0309 re\u0300n luy\u00ea\u0323n ki\u0303 n\u0103ng theo y\u00eau c\u00e2\u0300u c\u00e2\u0300n \u0111a\u0323t. V\u1eadn d\u1ee5ng 4. M\u1eb7t c\u1eaft c\u1ee7a m\u1ed9t li gi\u1ea5y QH KP \u0111\u1ef1ng b\u1ecfng ng\u00f4 c\u00f3 d\u1ea1ng h\u00ecnh thang c\u00e2n MNPQ (H\u00ecnh 13) v\u1edbi hai \u0111\u00e1y MN = 6 cm, PQ = 10 cm v\u00e0 \u0111\u1ed9 d\u00e0i hai \u0111\u01b0\u1eddng ch\u00e9o MP = NQ = 8 2 cm. M N T\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng cao v\u00e0 c\u1ea1nh b\u00ean H\u00ecnh 13 c\u1ee7a h\u00ecnh thang. \u2013 M\u1ee5c \u0111\u00edch c\u1ee7a V\u1eadn d\u1ee5ng 4: HS c\u00f3 c\u01a1 h\u1ed9i v\u1eadn d\u1ee5ng ki\u1ebfn th\u1ee9c v\u1eeba h\u1ecdc v\u00e0o th\u1ef1c t\u1ebf, v\u1eadn d\u1ee5ng t\u1ed5ng h\u1ee3p c\u00e1c k\u0129 n\u0103ng th\u00f4ng qua vi\u1ec7c t\u00ednh \u0111\u1ed9 d\u00e0i \u0111\u01b0\u1eddng cao v\u00e0 c\u1ea1nh b\u00ean c\u1ee7a m\u1eb7t c\u1eaft c\u1ee7a m\u1ed9t li gi\u1ea5y \u0111\u1ef1ng b\u1ecfng ng\u00f4 c\u00f3 d\u1ea1ng h\u00ecnh thang. 94","\u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c V\u1eadn d\u1ee5ng 4: HS tra\u0309 l\u01a1\u0300i y\u00eau c\u1ea7u v\u00e0o v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. GV c\u00f3 th\u1ec3 t\u1ed5 ch\u1ee9c cho HS l\u00e0m vi\u1ec7c nh\u00f3m ho\u1eb7c thuy\u1ebft tr\u00ecnh. H\u01b0\u1edbng d\u1eabn \u2013 \u0111\u00e1p \u00e1n: MH = NK = 8 cm, MQ = NP = 2 17 cm. IV. H\u01b0\u1edbng d\u1eabn gi\u1ea3i c\u00e1c b\u00e0i t\u1eadp 1. a) x = 40o; \t\t\t b) x = 120o, y = 70o;\t\t\t c) x = 36o; \t\t\t d) x = 60o. 2. Ta c\u00f3 AB = AD, suy ra tam gi\u00e1c ABD c\u00e2n t\u1ea1i A, A D 1 suy ra B\uf0b51 = D\uf0b51. \t (1) C Ta l\u1ea1i c\u00f3 BD l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a B\uf0b5, suy ra B\uf0b51 = B\uf0b5 2.\t (2) 1 2 M T\u1eeb (1) v\u00e0 (2) suy ra B\uf0b5 2 = D\uf0b51. C B Suy ra BC \/\/ AD (c\u00f3 c\u1eb7p g\u00f3c so le trong b\u1eb1ng nhau). V\u1eady t\u1ee9 gi\u00e1c ABCD l\u00e0 h\u00ecnh thang.\t 3. a) Ta c\u00f3 BC v\u00e0 MN c\u00f9ng vu\u00f4ng g\u00f3c v\u1edbi AH, N A suy ra MN \/\/ BC. Suy ra t\u1ee9 gi\u00e1c BCMN l\u00e0 h\u00ecnh thang. 1 1 b) Ta c\u00f3 MN \/\/ BC, suy ra B\uf0b5 2 = M\uf0b51 (hai g\u00f3c so le trong). 2 H Ta c\u00f3 B\uf0b51 = B\uf0b5 2 (BM l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a B\uf0b5 ). Suy ra B\uf0b51 = M\uf0b51. Do \u0111\u00f3 tam gi\u00e1c BNM c\u00e2n t\u1ea1i N. B Suy ra BN = MN.\t 4. a) X\u00e9t \u0394ABD v\u00e0 \u0394EBD, ta c\u00f3: A BD l\u00e0 c\u1ea1nh chung, BA = BE, B\uf0b51 = B\uf0b5 2. F 11 D Suy ra \u2206ABD = \u2206EBD (c.g.c). 22 b) \u2206ABD = \u2206EBD, suy ra B\uf0b7ED = B\uf0b7AD = 90o. 1 I Do \u0111\u00f3, tam gi\u00e1c EBD vu\u00f4ng t\u1ea1i E, 2 HE C suy ra DE \u22a5 BC. B Ta l\u1ea1i c\u00f3 AH \u22a5 BC. Suy ra DE \/\/ AH. V\u1eady t\u1ee9 gi\u00e1c ADEH l\u00e0 h\u00ecnh thang vu\u00f4ng.\t c) Ta c\u00f3 \u2206IDA = \u2206IDE (c.g.c), suy ra \uf024I1 = \uf024I2. Ta c\u00f3 AI \/\/ DE, suy ra \uf024I1 = D\uf0b5 2 (hai g\u00f3c so le trong). Ta l\u1ea1i c\u00f3 D\uf0b51 = D\uf0b5 2, do \u0111\u00f3 D\uf0b51 = \uf024I2. Suy ra AD \/\/ EF v\u00e0 EF \u22a5 AB. V\u1eady t\u1ee9 gi\u00e1c ACEF l\u00e0 h\u00ecnh thang vu\u00f4ng. 5.\t T\u1ee9 gi\u00e1c GKIH kh\u00f4ng ph\u1ea3i l\u00e0 h\u00ecnh thang c\u00e2n v\u00ec kh\u00f4ng c\u00f3 hai g\u00f3c k\u1ec1 m\u1ed9t \u0111\u00e1y b\u1eb1ng nhau. T\u1ee9 gi\u00e1c MNPQ c\u00f3 MQ \/\/ NP, N\uf0b5 = P\uf024 = 75o. Suy ra MNPQ l\u00e0 h\u00ecnh thang c\u00e2n. T\u1ee9 gi\u00e1c ABCD c\u00f3 AB \/\/ CD, AC = BD. Suy ra ABCD l\u00e0 h\u00ecnh thang c\u00e2n. 95","6. Trong h\u00ecnh thang c\u00e2n ABCD, DC ta c\u00f3 \u2206ABD = \u2206BAC (c.g.c). Suy ra A\uf0b51 = B\uf0b51. Ta l\u1ea1i c\u00f3 FG \/\/ AB, suy ra A\uf0b51 = E\uf0b51 (hai g\u00f3c \u0111\u1ed3ng v\u1ecb) F 2E 1 G v\u00e0 B\uf0b51 = E\uf0b5 2 (hai g\u00f3c so le trong). Suy ra E\uf0b51 = E\uf0b5 2. 2 V\u1eady EG l\u00e0 tia ph\u00e2n gi\u00e1c c\u1ee7a C\uf0b7EB. 1 1 A B 7. Trong tam gi\u00e1c vu\u00f4ng ADE, ta c\u00f3: DE = AD2 \u2212 AE2 = 612 \u2212 602 = 11 (cm), AB = DC \u2013 2DE = 92 \u2013 2 . 11 = 70 (cm). B\u00e0i 4. H\u00ccNH B\u00ccNH H\u00c0NH \u2013 H\u00ccNH THOI I. M\u1ee5c ti\u00eau 1. Y\u00eau c\u1ea7u c\u00e2\u0300n \u0111a\u0323t: \u2013 Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c t\u00ednh ch\u1ea5t v\u1ec1 c\u1ea1nh \u0111\u1ed1i, g\u00f3c \u0111\u1ed1i, \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh. \u2013 Nh\u1eadn bi\u1ebft \u0111\u01b0\u1ee3c d\u1ea5u hi\u1ec7u \u0111\u1ec3 m\u1ed9t t\u1ee9 gi\u00e1c l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh (v\u00ed d\u1ee5: t\u1ee9 gi\u00e1c c\u00f3 hai \u0111\u01b0\u1eddng ch\u00e9o c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng l\u00e0 h\u00ecnh b\u00ecnh h\u00e0nh). \u2013 Gi\u1ea3i th\u00edch \u0111\u01b0\u1ee3c t\u00ednh ch\u1ea5t v\u1ec1 \u0111\u01b0\u1eddng ch\u00e9o c\u1ee7a h\u00ecnh thoi. \u2013 Nh\u1eadn bi\u1ebft \u0111\u01b0\u1ee3c d\u1ea5u hi\u1ec7u \u0111\u1ec3 m\u1ed9t h\u00ecnh b\u00ecnh h\u00e0nh l\u00e0 h\u00ecnh thoi (v\u00ed d\u1ee5: h\u00ecnh b\u00ecnh h\u00e0nh c\u00f3 hai \u0111\u01b0\u1eddng ch\u00e9o vu\u00f4ng g\u00f3c v\u1edbi nhau l\u00e0 h\u00ecnh thoi). 2. N\u0103ng l\u1ef1c ch\u00fa tr\u1ecdng: t\u01b0 duy v\u00e0 l\u1eadp lu\u1eadn to\u00e1n h\u1ecdc, m\u00f4 h\u00ecnh ho\u00e1 to\u00e1n h\u1ecdc, giao ti\u00ea\u0301p toa\u0301n ho\u0323c. 3. T\u00edch h\u1ee3p: To\u00e1n h\u1ecdc v\u00e0 cu\u1ed9c s\u1ed1ng, t\u00edch h\u1ee3p c\u00e1c m\u00f4n h\u1ecdc kh\u00e1c. II. M\u1ed9t s\u1ed1 ch\u00fa \u00fd 1. GV c\u1ea7n \u00f4n t\u1eadp v\u00e0 c\u1ee7ng c\u1ed1 c\u00e1c ki\u1ebfn th\u1ee9c v\u1ec1 hai g\u00f3c so le v\u00e0 hai g\u00f3c \u0111\u1ed3ng v\u1ecb, \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a \u0111o\u1ea1n th\u1eb3ng v\u00e0 c\u00e1c tr\u01b0\u1eddng h\u1ee3p b\u1eb1ng nhau c\u1ee7a tam gi\u00e1c \u0111\u1ec3 gi\u00fap HS kh\u00e1m ph\u00e1 c\u00e1c t\u00ednh ch\u1ea5t c\u1ee7a h\u00ecnh b\u00ecnh h\u00e0nh v\u00e0 h\u00ecnh thoi. 2. GV s\u1eed d\u1ee5ng c\u00e1c h\u00ecnh \u1ea3nh quen thu\u1ed9c trong th\u1ef1c t\u1ebf \u0111\u1ec3 gi\u00fap HS nh\u1eadn bi\u1ebft h\u00ecnh b\u00ecnh h\u00e0nh v\u00e0 h\u00ecnh thoi. 96","III. G\u1ee3i \u00fd c\u00e1c ho\u1ea1t \u0111\u1ed9ng c\u1ee5 th\u1ec3 AB DC H\u0110K\u0110 Quan s\u00e1t h\u00ecnh ch\u1ee5p c\u00e1c m\u00e1i nh\u00e0 \u1edf ph\u1ed1 c\u1ed5 H\u1ed9i An, em th\u1ea5y c\u00e1c c\u1ea1nh \u0111\u1ed1i c\u1ee7a t\u1ee9 gi\u00e1c ABCD c\u00f3 g\u00ec \u0111\u1eb7c bi\u1ec7t? \u2013 M\u1ee5c \u0111\u00edch cu\u0309a H\u0110K\u0110: Gi\u00fap HS co\u0301 c\u01a1 h\u00f4\u0323i tr\u1ea3i nghi\u1ec7m, tha\u0309o lu\u00e2\u0323n v\u1ec1 vi\u1ec7c nh\u1eadn bi\u1ebft c\u00e1c h\u00ecnh \u1ea3nh trong th\u1ef1c t\u1ebf c\u00f3 d\u1ea1ng h\u00ecnh b\u00ecnh h\u00e0nh, h\u00ecnh thoi. C\u00e1ch \u0111\u1eb7t v\u1ea5n \u0111\u1ec1 n\u00e0y c\u00f3 kh\u1ea3 n\u0103ng thu h\u00fat HS v\u00e0o b\u00e0i h\u1ecdc. \u2013 G\u01a1\u0323i y\u0301 t\u00f4\u0309 ch\u01b0\u0301c H\u0110K\u0110: GV n\u00eau c\u00e2u h\u1ecfi, HS tra\u0309 l\u01a1\u0300i, l\u01a1\u0301p nh\u1eadn x\u00e9t, GV s\u1eed d\u1ee5ng c\u01a1 h\u1ed9i \u0111\u1ec3 gi\u1edbi thi\u1ec7u b\u00e0i. L\u01b0u \u00fd: \u0110\u00e2y l\u00e0 c\u00e2u h\u1ecfi m\u1edf, t\u1ea1o s\u1ef1 ch\u00fa \u00fd v\u00e0 k\u1ebft n\u1ed1i. GV kh\u00f4ng c\u1ea7n \u0111\u00e1nh gi\u00e1 c\u00e2u tr\u1ea3 l\u1eddi c\u1ee7a HS \u0111\u00fang hay sai. Tinh th\u1ea7n chung c\u1ee7a H\u0110K\u0110 l\u00e0 m\u1ecdi c\u00e2u tr\u1ea3 l\u1eddi \u0111\u1ec1u \u0111\u01b0\u1ee3c ghi nh\u1eadn, mu\u1ed1n bi\u1ebft \u0111\u00fang \u2013 sai, h\u1ecdc xong b\u00e0i n\u00e0y s\u1ebd r\u00f5! 1. H\u00ecnh b\u00ecnh h\u00e0nh \u0110\u1ecbnh ngh\u0129a H\u0110KP 1 97","T\u00ednh ch\u1ea5t H\u0110T\u00edKnPh 2ch\u1ea5t 2 Cho t\u1ee9 gi\u00e1c ABCD c\u00f3 c\u00e1c c\u1ea1nh \u0111\u1ed1i song song. G\u1ecdi O A B l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng ch\u00e9o. H\u00e3y ch\u1ee9ng t\u1ecf: 1 1 \u2013 Tam gi\u00e1c ABC b\u1eb1ng tam gi\u00e1c CDA. O \u2013 Tam gi\u00e1c OAB b\u1eb1ng tam gi\u00e1c OCD. 11 DC H\u00ecnh 3 \u2013 M\u0110\u1ee5\u1ecbcn\u0111h\u00edcl\u00edh cu\u0309a H\u0110KP 1, 2: Gi\u00fap HS co\u0301 c\u01a1 h\u00f4\u0323i tr\u1ea3i nghi\u1ec7m, tha\u0309o lu\u00e2\u0323n v\u1ec1 \u0111\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh chT\u1ea5rto\u0111n\u1eb7gcht\u00ecrn\u01b0hnbg\u00ecnch\u1ee7ah\u00e0hn\u00ecnhh: b\u00ecnh h\u00e0nh qua vi\u1ec7c quan s\u00e1t m\u1ed9t th\u01b0\u1edbc v\u1ebd truy\u1ec1n v\u00e0 so s\u00e1nh c\u00e1c tam\u2013 Cgi\u00e1\u00e1cccb\u1ea1\u1eb1nnhg\u0111\u1ed1nihba\u1eb1un. g nhau. \u2013 G\u2013\u01a1\u0323iCy\u00e1\u0301ct\u00f4g\u0309\u00f3cch\u0111\u01b0\u0301\u1ed1ciHb\u1eb1\u0110nKg Pnh1a,u2. : GV n\u00eau c\u00e2u h\u1ecfi, HS tra\u0309 l\u01a1\u0300i, l\u01a1\u0301p nh\u1eadn x\u00e9t, GV \u0111a\u0301nh gia\u0301. Th\u1ef1\u2013cHha\u00e0in\u0111h\u01b0\u1edd1n.gCchh\u00e9oohc\u00ec\u1eafnthnhba\u00ecnuht\u1ea1hi \u00e0trnuhngP\u0111Qi\u1ec3RmS c\u1ee7a m\u1ed7i \u0111\u01b0\u1eddng. S P v\u1edbi I l\u00e0Vg\u00ed ida\u1ee5o 2\u0111.iT\u1ec3m\u00ecm cc\u1ee7\u00e1ca \u0111hoa\u1ea1in\u0111t\u01b0h\u1eb3\u1eddnnggvc\u00e0hc\u00e9\u00e1oc g(H\u00f3c\u00ecnbh\u1eb1n4g).nhau c\u00f3 trong h\u00ecnh c\u1ee7a 2I . H\u00e3y ch\u1ec9 ra c\u00e1c \u0111o\u1ea1n th\u1eb3ng b\u1eb1ng nhau v\u00e0 c\u00e1c g\u00f3c Gi\u1ea3i b\u1eb1ng nhau c\u00f3 trong h\u00ecnh. M\u1ee5Tcro\u0111n\u00edcghh\u00eccn\u1ee7hab\u00ecTnhh\u1ef1hc\u00e0nhh\u00e0AnBhC1D: vH\u1edbSi Othl\u00e0\u01b0\u0323gciahoa\u0300\u0111nih\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng ch\u00e9o, ta c\u00f3: Q nh\u1eadn bAi\u1ebfBt h=\u00ecnChDb;\u00ecAnhDh=\u00e0nBhC\u0111;\u1ec3OrA\u00e8n=luOyC\u1ec7;nOkB\u0129 n=\u0103nOgDth; eo P R H\u00ecnh 4 Q y\u00eauVc\u00f3c\u1ead\u1ea7nduDB\uf0b7\uf0b7\u1ea1dAcnA\u1ee5\u1ea7gDCnnhg==\u0111\u00ecn\u1ea11BA\uf0b7\uf0b7ht..CCMtD\u1ee9B\u1eaf;;gtAA\uf0b7\uf0b7il\u00e1\u01b0BBc\u1edbDCicc\u00f3==\u1ee7caAB\uf0b7\uf0b7\u00e1mDDc CC\u1ed9ct\u1ea1;;nlDB\uf0b7\u01b0\uf0b7h\u1edbAB\u0111iCC\u1ed1bi\u00f3==nsABo\uf0b7\uf0b7gnDCcghADus;;oyn\u1ec1ng S (H\u00ecnA\uf0b7hO5B). =ChC\uf0b7oObDi\u1ebf;tA\uf0b7\u0111O\u1ed9 dD\u00e0i=hC\uf0b7aiOcB\u1ea1;nhA\uf0b7cO\u1ee7Ca t=\u1ee9B\uf0b7gOi\u00e1Dc .n\u00e0y l\u00e0 4 cm v\u00e0 5 cm. T\u00ecm \u0111\u1ed9 d\u00e0i hai c\u1ea1nh c\u00f2n l\u1ea1i. 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M \u2013 MV\u1ee5\u1eadcn\u0111\u00eddc\u1ee5hncg\u1ee7a2V. \u1eadMn d\u1eb7t\u1ee5ntgr\u01b01\u1edb,c2:cG\u1ee7ai\u00fapm\u1ed9t HG HS c\u00f3c\u00f4cn\u01a1ght\u1ed9r\u00ecinvh\u1eadnx\u00e2dy\u1ee5dn\u1ef1gngki\u1ebf\u0111n\u01b0\u1ee3tch\u1ee9lc\u00e0mv\u1eebba\u1eb1ng H\u00ecnh 6 H\u00ecnh 5 h\u1ecdc v\u00e0ko\u00ednthh\u1ef1cc\u00f3t\u1ebfd,\u1ea1nnhg\u1eadnh\u00ecbnih\u1ebftbc\u00ecn\u00e1ch hh\u00ec\u00e0nnhhbE\u00ecnFhGH h\u00e0nh cv\u0169\u1edbnigMnhl\u01b0\u00e0 sg\u1eediaod\u1ee5\u0111nig\u1ec3mt\u00ednch\u1ee7achh\u1ea5ati c\u0111\u1ee7\u01b0a\u1eddng h\u00ecnh bc\u00ecnhh\u00e9oh\u00e0(Hnh\u00ecnthro6n)g. tC\u00ednhho tboi\u00e1\u1ebfnt.EF = 40 m, E F \u2013 GE\u01a1\u0323Mi y\u0301=t\u00f43\u0309 6chm\u01b0\u0301,cHVM\u1eadn=d1\u1ee56ngm1. ,T2\u00edn:hH\u0111S\u1ed9tdra\u00e0\u0309il\u01a1\u0300i y\u00eau c\u1ea7u v\u00e0o v\u1edf, GV s\u1eeda chung tr\u01b0\u1edbc l\u1edbp. 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B F J 60o E A C I 60o K M 120o D H G L a) b) S c) Q T Z 80o O V 75o Y PN 100o 70o 105o d) U R X e) g) H\u00ecnh 9 M\u1ee5c \u0111\u00edch c\u1ee7a Th\u1ef1c h\u00e0nh 2: HS th\u01b0\u0323c ha\u0300nh nh\u1eadn bi\u1ebft h\u00ecnh b\u00ecnh h\u00e0nh \u0111\u1ec3 r\u00e8n luy\u1ec7n k\u0129 n\u0103ng theo y\u00eau c\u1ea7u c\u1ea7n \u0111\u1ea1t. 99"]