!!!!!!!!!!!!!!!!!!!!!!! 1!!!!!!!!!!!!!!!!! 1 1 1 1!!!!!!!!!!!!!!!! 1 1 1 1!!!!!!!!!! 1 1 2 18!!!!!!!!!! 1 2 33!!!!!!!!!!!!! 1 2 1!!!!!!!!!!!!!!!! 33 1 2 2!!!!!!!!!!!!!!!! 52 1 2 3!!!!!!!!!!!!!!! 67 1 3!!!!!!!!!!!!!!!!!!! 86 1 4!!!!!!!!!!!!!!!!!! 102 1 5 118!!!!!!!!!!!!!!! 1 6!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 127 131 141!!!!!!!!!!!!!!!!! 148 2 1 148!!!!!!!!!!!!!!!! 2 2 161!!!!!!!!!!!!! 2 3 176!!!!!!!!!!!!! 2 4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 189 198 203!!!!!!!!!!!!!!!!!!!!! 210!!!!!!!!!!!!!!!!! 210
ONTNTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 212 213 215 218 221 224 227
1 1 1 1 1 学习指导 1 2 1 2 知识点精析 1 1 1 2 2 1
2 1-1-1 3 2 1 2 3 3 1 1-1-1 2 1 2 1 2 3 4 1 1-1-2 S = = F 2 1-1-2 问题探究 1-1-3 1 = = 180 = = 2 1-1-3 = = 3 = = = F
解题方法指导 1 2005 1-1-4 = 110 F F 1 + F = 110 30 50 70 2 135 1-1-4 F 1 + F F F = = = 110 2 1, = = 110 F =, F = 110 + F + F = 180, + F = 70 2 1-1-5 F F = 135 = F = 90 + + F + F = 360, = 45, = = 45, + = 180, = 135 =, = 135 45 135 45 135 F 1-1-5 3
2 1-1-6 50 cm O O O 7 cm O 1-1-6 O = O O = O O O 50 cm, = = O= O + + + = 50, + = 25 1 O+ O + - O + O + = 7, - = 7 2 1 2 = 16 = 9 建立关于平行四边形两邻边长的方程组是解这类题的关键 = 16 cm = 9 cm = 16 cm = 9 cm 3 1-1-7 F F F = 60 = 2 cm F = 3 cm F 1-1-7 F = 60 F = 120 4
= = 60 = F = 30 F 30 F F F, = F = 90 F F = 60, = 360 - - F - F = 120 360,, + = 180 + = 180, = = 60, = F = 30, = 2 = 2 2 = 4 cm = 2F = 2 3 = 6 cm, = 槡 2-2 = 槡 4 2-2 2 30 = 槡 12 = 2 槡 3 cm F = 槡 2 - F 2 = 6 2 2 槡 - 3 = 3 槡 3 cm, = 2 + = 2 4 + 6 = 20 cm, S = = 6 2 槡 3 = 12 槡 3 cm 2 S = F = 4 3 槡 3 = 12 槡 3 cm 2 4 2005 1-1-8 F = F = F F 1-1-8 5
6 F F F F F, =, = F F { = = F = F, F SS F, = F 5 1-1-9 O F F O F 1-1-9 F O F O OF = F = = F O, O= O F, O = FO O OF { O = FO O = O O = OF, O OF S S O OF
, = F =, - = F - = F 1 2 O = OF = F 基础达标演练 1 = 35 = = 2 20 cm 18 cm 3 2006 1-1-10 MN M M = 6 M N NM 1-1-10 N = M 4 O O O 3 cm 22 cm = 7 = 5 : : : 1: 2: 3: 4 1: 2: 2: 1 2: 1: 2: 1 2: 2: 1: 1 N 6 2005 1-1-11 1 + 2 = 180 2 + 3 = 180 3 + 4 = 180 2 + 4 = 180 7 2005 1-1-12 O O O 1 2 3 4 1 2 3 4 1-1-11 O 1-1-12 1-1-13
8 2004 1-1-13 = 100 100 80 60 40 9 1-1-14 S = 6 cm 2 5 cm 2 4 cm 2 3 cm 2 1-1-14 F 1-1-15 1-1-16 10 2005 1-1-15 F F = F 11 2005 1-1-16 F = F = F 12 2005 1-1-17 F F G H 1 2 F F G H F 1-1-17 1-1-18 8 F 1-1-19 13 2005 1-1-18 F 1 = F 2 F = F 14 1-1-19 F
F 1 F 2 F F 答案与提示 1 145 35 = + = 180 2 8 cm 2 3 12 = N = M 9 N= M = M = M 12 4 7 cm 4 cm - = 3 cm + = 11 cm 5 6 7 8 + = 180 9 MN GH 8 10, =, = F F F, = F = 90 F S, = F 11 = = = F F SS, = F 12 1 G H H FG G H F 2, { = = = =, = 13 1, F, F = F = =, F, = F 2 = 2 F = F =
= F = 2, = + F = F, F = F 14,, = = 1 S = S F, F, F F, F = F 2, F, = = 1 2 3 + + F = + + F 难点指津 3 1 3 4 1-1-20,, 2 = 3 3, 1 = 2, 1 = 3, = = 3, 1 = + + + = 3 + 7 + 3 + 7 = 20 2 1-1-20 3 4,, 2 = 3, 1 = 2, 1 = 3, = = = 3 = + + + = 3 + 7 + 3 + 7 = 20 = = 4 = + + + = 4 + 7 + 4 + 7 = 22 2 10
综合延伸 6 1-1-21 Q N N Q N Q N P Q N M P M Q 1-1-21 Q N Q Q P M Q Q,, + = 180 Q Q, Q = 1 2 Q= 1 2, Q + Q= 1 2 + 1 = 90 2, Q = 90, Q Q 11
7 2600 1-1-22 375 km 125 km 100 km 14 L 3 8 800 12 1-1-22 100 km = 375 = + 125, = 375 + 125 = 500, = =, 2 + = 2 375 + 500 = 1750, 1750 14 100 = 245 L 14 100, 245 3 8 = 931, 931 + 800 = 1731 1731 < 2600, 2600-1731 = 869 2600 100 km 14 L 1 km 14 L
8 2005 a b P Q a M N b 1 1-1-23 PM QN a b PMNQ PM = QN 1-1-23 1-1-24 1-1-23 a b P Q a a a M 1-1-23 N b 1-1-24 b 1-1-25 2 a b 1-1-25 a b 1 1 1-1-26 2 1-1-27 M P N 1-1-26 Q a b P M 1-1-27 Q N a b b 你还能找出更多的直线段相等 曲线段相等的例子吗 1 13
思维拓展测试 1 1-1-28 F F 2 1 1-1-29 1 1 F 1 1-1-28 M 1 N 1 2 1-1-29 2 2 F 2 M 2 N 2 3 1 F 1 2 F 2 n F n M 1 N 1 M 2 N 2 M n N n F M 1 1 F 1 M 1 M 2 1 F 1 2 F 2 N 1 1 1-1-29 N 1 N 2 2 F 1-1-30 3 1-1-30 F F 4 1-1-31 1 FG P MP F F F G 1 G H 2 G N H 3 1-1-31 1-1-31 2 G F G PH P H H PG H PG 14
1-1-31 3 G F G PH P H P M GH N MN 5 2005 1-1-32 = 4 cm = 60 P 1 cm P PM PM 1 P 2 PM P 2 P 2 Q 1 cm M 2 cm Q QN PM Q t P 0 t 10 PM QN 1-1-32 S cm 2 t S 答案与提示 1 = F F = = F F 2 1 9 2 36 3 1 + 2 + 3 + + n + 1 2 n + 1 2 n + 2 2 = 4 1 M 1 M 1 n = 1 9 2 6 6 1 + 2 + 3 1 + 2 + 2 36 M 1 M 2 M n 1 + 2 + 3 + + n + 1 1 2 n 1 + 2 + 3 + + n + 1 1 + 2 + 3 + + n + 1 2 n + 1 2 n + 2 2 4 3 1 = F 1 = F F 2 = F F F 4 PH G PH G h, S FG = 1 2 G h S HG = 1 2 G h, S FG = S HG 15
S G + S FG S G + S HG, 5 1 P 2 P = 2 cm = 60 = 1 P = 槡 3, S P = 槡 3 2 2 0 t 6 P Q PM QN F Q = t F = 1 2 t QF = 槡 3 2 t P = t + 2 = 1 + 1 2 t P = 槡 3 + 槡 3 2 t, S = 槡 3 2 t + 槡 3 2 6 t 8 P Q PM QN F Q = t F = 1 2 t F = 4-1 2 t QF = 槡 3 2 t P = t - 6 P = 10 - t P = 10 - t 槡 3 = 4 槡 3 S = - 5 槡 3 8 t2 + 10 槡 3t - 34 槡 3 8 t 10 P Q PM QN F Q = 20-2t QF = 20-2t 槡 3 P = 10 - t P = 10 - t 槡 3 3, S = 槡 3-30 槡 3t + 150 槡 3 t S 槡 3 2 t + 槡 3 2 0 t 6 S = 5 - 槡 3 8 t2 + 10 槡 3t - 34 槡 3 6 t 8 3 槡 3-30 槡 3t + 150 槡 3 8 t 10 2 t2 2 t2 16
视野情境扫描 1-1-33 1 1-1-33 1 360 1 1-1-33 1-1-33 2 O O' O' O 2 O 17
1 1 2 学习指导 1 2 3 1 2 知识点精析 1 1 2 3 4 5 2 18
1 3 2 3 4 5 3 1 2 3 4 5 1 2 问题探究 1-1-34 1-1-34 O 1-1-35 O 1-1-35 = = 2 O = O O = O 5 19
解题方法指导 1 1-1-36 M N P Q M = N = P = Q M MNPQ Q P N 1-1-36 MQ PN MN QP = PN MN = PQ MNPQ, = = = = M = N = P = Q, M = P Q = N MQ PN M = P = { Q = N, MQ PN SS, MQ = PN MN PQ, MN = PQ, MNPQ 20
2 2005 1-1-37 F F = F = F F 1-1-37 F = F = F, F = F { F = F = F =, F SS, = F =, =, 3 1-1-38 1 = 2 = 30 3 = 4 = 38 F 4 2 3 F 1-1-38 1 21
= = 1 = 2 = 30 3 = 4 = 38, 1 + 3 = 68 2 + 4 = 68, = 180-2 + 4 = 180-68 = 112 = 180-1 + 3 = 180-68 = 112, = F, F = 3 = 38 F = 4 = 38, 2 + F = = 30 + 38 = 68 1 + F = = 30 + 38 = 68, =, 4 1-1-39 F = F F F O 1-1-39 = F O O = OF O, O= O O = O 22
= F O + O = OF + O, O = OF O= O, F 5 1-1-40 M N M = N M NF F MN F 1 M 1-1-40 N 2 F MNF M NF M FN M = FN M NF N MF,, 1 = 2 M NF, M NF M = NF = 90 M NF { M = NF 1 = 2 M = N, M NF S, M = NF, M = NF 23
, MFN, MN F 6 1-1-41 = F M N F FM = N M F N 1-1-41 FM = N FM N FM N F FM F, = F = F, - = - F = F, F, = F F M NF M N F, M = NF, MFN, FM = N 7 24
F 1 2 3 F 1-1-42 1-1-42 1 2 3 = 4 基础达标演练 1 3: 2: 3: 2 2 a b c d a 2 + b 2 + c 2 + d 2 = 2ac + 2bd 3 3 cm 5 cm 7 cm 4 F F = F 5 1-1-43 O F O O O = OF O = F F O 1-1-43 1-1-44 6 2005 1-1-44 F F 25
26 7 = = = = = = = 8 = = = 9 F F F F = F F = 3 5 F = 2 5 10 1 2 3 4 11 2006 1-1-45 = 1 2 = 12 1-1-46 G H G = H F = HFG 1-1-45 G F H 1-1-46 F 1-1-47 13 1-1-47 = = F = F = F 14 1-1-48 F F 15 1-1-49 = F = F = F F
F 1-1-48 27 F 1-1-49 1-1-50 16 1-1-50 F = F 1 F 2 = 7 cm F 答案与提示 1 2 a 2 + b 2 + c 2 + d 2 = 2ac + 2bd a - c 2 + b - d 2 = 0 a = c b = d 3 6 3 2 4 5 O F 6 = F 7 8 = 9 10 11, = 1 2 = 1 2, =, =,, = 12,, = F = G = H, FG H, FG = H FG = H, FGH = HG, FG H, HFG 13 = =,,, = = F, F, = F 14 F, = F
, F = 1 2 F = 1 2, F = F, F = F F =, F =, = F, F, F 15 F =, = =, =, =, F = F =, = 1 2 F, = 1 2 = 1 2, F =, F 16 1 O, O = O O = O O = + O OF = F + O = F, O = OF, F 2 F, F = = 7 cm 难点指津 1 2 综合延伸 8 1-1-51 = 60 F = 2 F = 槡 3F 2 1 1-1-51 28
= 90 = F = F = 1 2 = 1 2, F =, F =, F, F = = 2 = 2, = = 60, = =, 1 = 1 2 2 = 30, = 90 Rt 2 = 2 + 2, 2 = 2-2 = 2 2-2 = 3 2, = 槡 3 = 槡 3F 9 O 5 1 2O= O 3 = 4 = 5 1 5 2 2 5 2 1 1 5 29
5 1 2 O O O= O O = O = 2 1 5 ⅰ 1 2 ⅱ 1 3 ⅲ 1 4 ⅳ 2 5 ⅴ 4 5 2 ⅰ 2 3 1-1-52 ⅱ 2 4 1-1-53 O 1-1-52 ⅲ 3 4 1-1-54 O 1-1-53 ⅳ 3 5 1-1-55 1-1-54 1-1-55 思维拓展测试 1 1 2 = 3 = 4 = 2 30 30
3 2005 1-1-56 O F F F = F = F = F = F O F F 1-1-56 1-1-57 1-1-58 4 1-1-57 45 5 1-1-58 > F 1 F 2 F 3 > < 答案与提示 1 1 3 2 3 3 F 4 F 180 1-1-59 Rt =, = 45, =, = = 45, F = = 45, F + = + = 180, F F = = 90, F 1-1-59 F = =, F = 45 5 1 F M M F 31
M = F MF 2 F + = F = - F + = 1 F = M = - M = - 3 F + = F + = 视野情境扫描 v 1 m/s 1-1-60 v 2 m/s M F 1 F 2 F 1 F 2 F F 1 F 2 1-1-61 v 1 F 1 F v 2 2km h 4km h 1-1-60 M F 2 1-1-61 1-1-62 1-1-62 2 km/h 4 km/h 32
1 2 1 2 1 学习指导 1 2 3 1 2 知识点精析 1 獉獉獉獉獉 2 1 2 3 1 2 3 1 2 3 33
1 2 4 1 2 5 = 1-2-1 O 1S O = S O = S O = S O = 1 4 S 2 S = S = S = S = 1 2 S 3 问题探究 O 1-2-1 1 1-2-2 1 = F = GH 2 1-2-22 1-2-2 3 1-2-23 1-2-24 1-2-22 3 34
解题方法指导 1 1-2-3 O O = 120 = 6 cm O 1-2-3 O= O O = 120 = 30 Rt 30, = h O= O = 1 2 O = O = 1 2, O= O O = 120, O= O = 30 = 90, = 2 = 2 6 = 12 cm 12 cm 2 2005 1-2-4 O F F F = F O 1-2-4 35
= F O OF F, = O= O = 1 2 O = O = 1 2, O = O F, O = FO = 90 O OF { O = OF O = FO O = O, O OF S, = F 3 1-2-5 F G H FGH + = 180 1 = 1 2 2 = 1 2, 1 + 2 = 1 + = 90 2 1 H G 1-2-5 F 2, = 90 36
G = 90 H = 90, GH = H = 90, FGH 4 1-2-6 MN Rt MN MN = M F F = F N 37 F 1-2-6 F F F = F = F F F F F F F F F, F = F = F = 90, M + N = 90 MN MN, M + = 90 = = 90, = N =,, = = = 90 F, = F = 45, + = F + N F = F
= F = F, F F, F = F 5 1 2005 1-2-7 F G H = 2 = 4 3 4 6 8 H F 1-2-7 G O 1-2-8 2 2005 1-2-8 F O F 1 5 1 4 1 3 3 10 F 1 H F GF GH S H = S F = S GF = S GH = 1 2 = 1 2 2 = 1 H = 1 = 2 2 S H = 1 2 8-4 = 4 1 2 = 1 S - 4 S H = 2 O FO 1 O O 4 1 4 1 2 1 38
2 6 1-2-9 O = 8 cm O O 1-2-9 = 8 cm O = O O= O O = O O, O = O, O= O = O = O =, = 8, O= O = O = O = = 4 = 90 2 = 2-2 2 = 8 2-4 2 = 48, = 4 槡 3 = 4 4 槡 3 = 16 槡 3 cm 2 60 基础达标演练 1 2005 O O = 2 O = 18 cm = cm 2 2005 1-2-10 k 2 k = 39
1-2-10 1-2-11 3 2005 1-2-11 4 O O = 110 O = 5 = 3 = 5 = 6 : = 7 4 cm 2 槡 3 cm cm 2 8 2: 3 3: 4 3: 5 4: 5 9 40 80 100 20 40 10 5 3 F F 2 3 5 3 5 11 1-2-12 : = 3: 2 O 12 18 22 36 12 O = = = 90 5 2 1-2-12 40
O = O O = O = = = 90 + = 180 = = = 90 13 2005 1-2-13 M 1 M M 2 M = M M 1-2-13 1-2-14 14 1-2-14 = 2 = 15 1-2-15 O = O O 1-2-15 1-2-16 16 1-2-16 O = O O = 75 17 1-2-17 = = 90 M N MN 18 1-2-18 = F F G F H HFG N M G F H 1-2-17 1-2-18 41
答案与提示 1 9 O = 2 O = 60 = 90 = 30 = 2 2 8 x y n ny = 2x x = 2y n = 4 k = 8 3 30 4 35 O= O 5 7 Rt = 4 = 3 = = 7 = 7 6 1: 2 = 1 2 7 2 4 槡 3 8 x y z z = x + 1 2 y 1 z2 = x 2 + y 2 2 1 2 x = 3 4 y x y = 3 4 9 10 F, = F = F, S = S F = S F = 1 3 S S = 1 2 S, S F = 5 2 11 = 90 : = 3: 2, = 54 = 36, = 54, = = 36, = - = 18 12 13 1, = = = 90 M = M, M M 2 M M, M= M, M = M 14 F F, = = 90, F, F = = 1 2 =, F = 1 2, F = 30, = = 1 2 180-30 = 75, = 90 - = 90-75 = 15 15,, 42
, = =, = 16 = O O = 75, O = 30, = 90, O = 60 O = O, O, O = 60 = O, =, = 45, = 60-45 = 15 17 M M Rt = 90 M, M = 1 2 M = 1 2, M = M N, MN 18, F = F, F, F = F =, = F, F, G FH, HFG, FH G H, H = 90, HFG 难点指津 1-2-19 M N = 2 MPNQ, = M N M, M P Q = N N, MN = N = N, N = N MN = N 1-2-19, P M MPN = 90 MQN = 90, PMQN MPN = MQN =90 PMQN PMQN 43
综合延伸 7 1-2-20 F O F F G O OG = 30 OG = 1 3 G 1-2-20 OG Rt O OG = 1 2 OG = 1 3 O = 1 2 O O F, = OG Rt O, OG = G = G OG = 30, OG = 30, = 90 Rt OG = 30, = 60 =, O = = 30 O = = 90 O, O, = O O = 1 2 30, = G = G = OG OG = 1 3 = 1 3 44
8 2005 1-2-21 F = 3 cm = 8 cm cm 2 F 1-2-21 F = 3 = = 8 = F = 5 F F, = = 8 = = 3 = 5 F, = F = F = 5 Rt F F = 槡 F 2-2 = 槡 5 2-3 2 = 4 F = x = F = x + 4 Rt F 2 + F 2 = F 2 8 2 + x 2 = x + 4 2 x = 6 F = 6 = S F + S F = 1 2 6 8 + 1 2 3 4 = 30 45
9 1-2-22 O O MN M F 3 O 1 O = OF 1 4 2 2 O F 1-2-22 N F 1 O = OF MN 2 = 3 1 = 2 O = O OF = O 2 F F = 90 F F 1 O = OF O= O 1 MN, 2 = 3 1 = 2, 1 = 3, O = O O = OF, O = OF 2 O= O F O= O O = OF, F F, 1 = 1 2 4 = 1 2, 1 + 4 = 1 2 + = 1 2 = 1 2 180 = 90, F 思维拓展测试 1 2005 1-2-23 46
FGH H = 3 F H = 5 M 2 1-2-24 = 6 cm = 9 cm N G 1 F 1-2-24 2 2 F F F F G 1-2-24 3 G cm 1-2-23 G 1 F 2 F 3 1-2-24 3 1-2-25 M M = M O P 1-2-25 M F 1-2-26 4 2006 1-2-26 = F F F F = 5 2005 120 cm 30 cm 80 cm 45cm 1-2-27 47
80 cm P H Q F 45 cm 1-2-27 1-2-28 6 2005 1-2-28 = 3 槡 3 = 6 F P Q PQ H P = 30 1 QF 2 PFH 7 1-2-29 > O O M N 1 S MN = S NM 2 MN MN 1 3 2 2 M: M N O P M 1-2-29 1-2-30 8 2005 P P 1-2-30 S P = S P + S P P F F S P + S P = 1 2 PF + 1 2 P F = 1 2 PF + P = 1 2 F = 1 2 S S P + S P + S P = 1 2 S, S P + S P = S P + S P + S P, S P = S P + S P 48
P 1-2-31 1 1-2-31 2 S P S P S P 49
P 1 P 2 答案与提示 1-2-31 1 30 FGH 2 2 3 = F = 3 = F = 3 G FG G = 1 2 3 = M + = 90 + = 90, O = O O = O =, = = M + PM = P + M P = PM = 45, M = M, M = =, = M 4, = 90 F, F = 90, = F, = F, =, F, = F 5 1-2-32 1-2-32 6 1 = x Rt P P = 30, P = 2x P = 槡 3x = P = 2x + =, 3x = 6 x = 2 = 2 50
, = 4 P = 2 槡 3, P= - P = 槡 3 Rt PH PH = 60, H = 3 PH = 2 槡 3, HQ = PQ - PH = 3 槡 3-2 槡 3 = 槡 3 Rt HQF QHF = 30, QF = 1 3 3 = 15 2 2 S F = 1 2 1 + 4 槡 槡 3 S HFQ = 1 2, S PFH = S PFQ - S HFQ = S F - S HFQ 15 = 槡 3 - 槡 3 = 7 2 2 槡 3 1 槡 3 = 槡 3 2 7 1 ON OM N = M N = M 2 MN 3 S 1 = 1 2 N = 1 2 M S 2 = 2 1 2 M = M S 2 = 1 2 S 1 M = 1 2 1 2 M M: M = 1: 4 8 1-2-33 1 S P = S P + S P 1-2-33 2 S P = S P - S P 1-2-33 P F F S P = 1 2 PF = 1 2 P + 1 2 F 1-2-33 P F = 1 2 P + 1 2 F = S P + 1 2 S S P + S P = S P + S = S P + 1 2 S, S P = S P + S P 51
视野情境扫描 槡 5-1 2 0 618 1-2-34 1-2-34 1-2-35 M M N 1-2-35 N 1-2-36 1-2-36 1-2-37 M M N 1-2-37 N 1-2-38 1-2-38 52
1 2 2 学习指导 2 5% ~ 8% 1 2 1 2 知识点精析 1 獉獉獉獉獉 2 1 2 3 3 1 2 3 1 3 3 53
4 a b S = 1 2 ab S = 1 ab 2 问题探究 1-2-39 4 1-2-391-2-3 O O F O 1 2 3 4 1-2-39 F F = F F F F = = = F O= O O = O F = OF = O F F F 解题方法指导 54
1 2005 1-2-40 15 cm = = 15 cm 1 1 = 55 1-2-40 = = =15 cm =60 =60 1 =120 120 2 24 cm 1:2 60 1-2-41 24, 6 + = 180 = 2, = 60 1-2-41 = 60,, = = 6 cm 6 cm 1: 2 1: 2 60 120 3 1-2-42 2 F H F G 1 H G F F 1-2-42
F = F G FG F = G G = 1 = G 2, 1 = 2 G, H = HG = 90 H = H, H HG, = G = 1 2, G = 1 2 =, G = 1 = G 2, F = G GF = G, G GF, G = FG G = G F F 4 1 2004 2 2005 O 1 = 2 3O= O 4O = O 5 6 1 2 5 56
1 2 1 2 6 3 4 5 6 1 2 1 2 6 3 4 5 3 4 6 5 2005 1-2-43 Rt = 90 = 60 F F = F 3 1 2 4 1-2-43 F F = = F F = = 1 = 30 = = F 3 = = 4 = 60 F, =, = 1 = 90 = 60, = 30, 1 = 30 2 = 60 60, 60, = = F =, F =,, 3 = = 60 3 = 4, 4 = 60 60, F 57
, F = F, = = F = F, F F 6 1-2-44 O F O F F = 2 cm = 4 cm F O 1-2-44 F F, O= O, FO = O OF = O, OF O, O = OF, F F, F, = = x = x = 4 - x Rt 2 = 2 + 2 x 2 = 2 2 + 4 - x 2 x = 2 5 = 2 5, S F = = 2 2 5 = 5 F 5 cm 2 基础达标演练 58
1 2004 1-2-45 = 65 = 2 2004 1-2-45 = 3 40 cm 12 cm 4 1-2-46 = 60 = 4 cm = = F 1-2-46 59 1-2-47 5 24 10 6 1-2-47 F F = F = 7 8 2004 1-2-48 = 80 F F F 80 70 65 60 9 8 4 cm 5: 1 1-2-48 4 2 cm 2 1 cm 1 05 cm 0 525 cm 10 = 120 : F 槡 3: 3 槡 3: 2 槡 3: 1 1: 2 11 1-2-49 = 4 cm
1 2 3 1-2-49 1-2-50 F H 1-2-51 12 1-2-50 = F = 60 = 20 F 13 2004 1-2-51 F = F 1 F 2 G F H G = 25 = 130 H 14 2006 1-2-52 F F 15 1-2-53 G F F O O F 1-2-52 1-2-53 1-2-54 16 1-2-54 F F = 400 m F = 300 m 60
答案与提示 1 50 = = = 65 2 2 3 3 96 cm 2 4 60 4 cm 4 槡 3 cm = 60 5 13 52 120 6 60 = 7 8 F = 40 = 100 F F = 40 F = 60 = F 9 180 5: 1 30 30 10 = 120, = 60, = = O O= 槡 3 2 = 槡 3, : = 槡 3: 3 11 1, =, =,,, = 60 2 = 120 2,, O = 1 2 = 1 2 = 1 2 4 = 2, O= 槡 2 - O 2 = 槡 4 2-2 3 S = 1 2 = 1 2 4 4 槡 3 = 8 槡 3 12, = 61 2 = 2 槡 3, = 2O = 4 槡 3 = 60,, = = 60 F = 60, = F = 20 = = F = 60, F, = F, F, F = 60 = + = 60 + 20 = 80, F = - F = 80-60 = 20
13 1, = = = = = F, F 2, = = 130 F, = F = 25, F = 80 G, H + F = 180, H = 100 14, F, = O = OF O= O, O OF, O = OF O= O, F F, F 15 F F, = F, S = = F, =, 16 F F, = F = F O = O OF = O = 90, FO = O, OF O, = F O = OF O = O F, F = 400, O = 1 2 = 200 F = 300, O = 150 Rt O = 槡 O 2 + O 2 = 250 S F = 1 F = 2, = 240 Rt =, S = 320 240 = 76800m 2 槡 2-2 = 70, = + = 320 难点指津 1 2 1 2 62
综合延伸 7 1-2-55 M N M =2 N M P P Q N M Q PMQN N 1-2-55 M N PMQN = 2 NM N M PMQN, = M N, M = N NM, M N N M, PMQN MN M = N, NM = 2 M, M = NM, N M, PMQN 63
8 2004 1-2-56 = F MF 1 F 3 4 2 M 1-2-56 MF MF M M F M = F M =, = M, 1 = 2 3 = 4, M F, M = F M = F, MF F, MF M = F M = F M = F 9 1-2-57 = 72 1-2-57 64
=72 = 72 = = 108 = 72 +36 72 36 1-2-58 72 36 36 36 72 36 36 72 36 36 72 36 72 36 72 36 36 36 72 36 36 72 72 36 72 36 36 72 36 36 36 72 72 72 72 72 36 36 1-2-58 36 72 2 36 + 72 2 = 180 思维拓展测试 1 O 1 = 90 2 3 = 4 5O = O 2 2004 1-2-59 F 2 5 P P P P PF F 3 2005 F F 1-2-59 F = = = 4 2004 a 60 a 1 2 a 槡 3 2 a 槡 3a 5 1-2-60 65
FG 60 60 120 120 G F 1-2-60 1-2-61 6 2004 1-2-61 1 2 3 7 1-2-62 1-2-62 F 1-2-63 8 1-2-63 F = F 1 F 2 F 9 1-2-64 O O F F 1 O OF O 2 F F 1-2-64 F 66
答案与提示 1 1 5 2 3 4 2 2 5 S FP = S P, S = 1 2 S 3 4 60 5 60 6 1-2-65 1-2-65 7 1 2 3 8 1 F 2 F = 60 F 60 F 9 1, O = O F, O = OF O = FO, O OF 2 F F O OF, = F =, + = F + = F F, F F, F 视野情境扫描 67
1-2-66 1-2-66 1 2 3 学习指导 1 2 1 2 68
知识点精析 1 1 2 2 1 2 3 1 2 1 2 问题探究 1 2 69
3 4 解题方法指导 1 1-2-67 = F F F 1-2-67 F = + = = 2, = 45, =45 =, =, = 1 = 22 5 2 F = + F, F = 90 + 22 5 = 112 5 70
2 1-2-68 F O G G O F G 1-2-68 OF = O OF = O O OF, O = O O = 90, O + O= 90 G, OF + G = 90, OF = O OF O { OF = O OF = O O = O, OF O, OF = O, F 3 1-2-69 F F = 45 F = + F 2 1 F G 1-2-69 71
F = + F F 90 G G = F G F F G F G, F = G 1 = 2 F = G F = 45, 1 + = 45, 2 + = 45 G = 45 F G { F = G F = G =, F G, F = G = + G = + F, F = + F 4 2005 O = = O = O = O = O = O = O O = O = O = O = O = O 72
5 1-2-70 FGH G P F 5 6 N 2 Q 3 4 1 H M FGH 1-2-70 FGH FGH, H F, 1 = 2 = 45 = 180-1 - 2 = 90 F = G = 90, FGH = 3 = 4 = 1 2 90 = 45, H F, H = F 1 = 2 = 45, =, H + = F + H = F, FGH FGH 基础达标演练 1 O = 2 O 2 = = 3 = 6 F G H = F = G = H= 2 S FGH = 4 O 73
16 cm = 5 2004 1-2-71 F F F 1-2-71 F 1-2-72 6 ' ' ' ' 1-2-72 = 槡 2 ' 7 2004 1-2-73 3 30 FG H H 8 1-2-74 F F = F F G = F G F F + = 90 F + G = 90 H F G G R P 1-2-73 1-2-74 74 F 1-2-75 Q 9 1-2-75 1 = P PQ Q PR R PQ + PR 1 2 槡 2 2 槡 3 2 2 3 10 1 2 3 4 1 2 3 4 11 = 1
槡 2 2 槡 2 2 槡 2 + 1 12 O = = = O = O = O = O F F = = 13 1-2-76 = MN M = 35 NM 45 55 65 75 14 1-2-77 = = 75 N F M 1-2-76 1-2-77 1-2-78 15 1-2-78 4 cm F F F 16 1-2-79 = F F = F = F F H 1-2-79 G 75 1-2-80 F G K 1-2-81 17 1-2-80 F G = G + F 18 1-2-81 FG G H H = K K = KFH F
答案与提示 1 2 + 2 槡 2 1 O 2 67 5 = 45 = 3 20 = 2 = 4 F = 4 S F = 1 2 2 4 = 4 H F GF HG S FGH = S - 4 S F = 36-16 = 20 4 4 O = 22 5 O = O = 45 = = 67 5 = = 4 5 = 90 F = = 90 F 6 槡 2-1 = 槡 2 1 1 1 2 槡 2 2 ' = 1 ' = 槡 2-1 7 槡 3 H H = 30 H = 1 2 H = 3 H = 槡 3 8 F 76 9 O O = 槡 2 2 P S 1 = 2 O = 1 2 PR + 1 2 PQ PR + PQ = O + 1 10 4 11 F F F = F = = 1 = 槡 2, = 槡 2 12 13 F MN F NM = F = F Rt F Rt F = M = 35 = 55 14 =, = = 75, = 30 = 90 =, = = 90 + 30 = 120, = 30 15, = 90, = 槡 2 + = 2 槡 5 S = 1 F = 8 2, F = 8 5 槡 5 cm 2
16 F, = 90 F = 90 = F F F, F F, F = F F= 90 F = 45, F = 45, F = F, = F, = F = F 17 H FG G H, GH F, GHF, H = G GH = F Rt G G + G = 90 G + = 90, G =, H = = H = 90 =, H, = H H = G+ GH = G+ F, = G+ F 18 KFH, = H = = 90 K = H, H K, H = K K = H H =, K + K = K +, = K = K = = F, K KF, K = KF KF HGF, KF = HF, H = K = F = HF, KFH K = KF FK + KF = 90, K + FK = 90, KF = 90, KFH 难点指津 1 + + + + + + 77
2 3 1 2 综合延伸 6 1-2-82 P P PF F P F 1 P = F 2 P F P H 1-2-82 F 1 P PF PF F = P P = P P 2 P F P F H PH + PH = 90 PF + FP = 90 PH = FP 1 P 78
, = 90, P = P P PF, P = PF = = 90, PF, P = F, P = F 2 P F P F H PF, PF = 90, PF + PF = 90 P = PF, P + PF = 90 P, P = PH P = P, PH + PF = 90, PH F P F 7 1-2-83 1 2 3 F F = F O H O F F 1-2-83 F F = 30 30 O = 1 2 F FH = O F FH H 79
O O = 1 2 = 1 2 FH, FH = O = 1 2 = 1 2 F, Rt FH FH = 30 30 F, 2 = 3 = 15, = 45, 1 = 15, 1 = 2 = 3 = 15 F 80 8 1-2-84 P Q F F P O 1 PQF 2 P Q 3 PQF 1-2-84 1 PQF 2 P = P P O 3 P Q F S = 1 2 P2 P P = 1 = = = P = Q = = F, P = Q = = F = = = = 90, FP PQ Q F
, FP = PQ = Q = F PF = PQ FPQ = 90, PQF 2 P O P =, P O, P 3 P PQF P PQF 9 1-2-85 1 1-2-85 2 100 H H Ⅰ Ⅰ M F F 200 G G N 200 200 F Ⅱ Ⅱ 100 1 2 1-2-85 FG M HG N S NH + S FM + S NMG = 200 100 2 + 100 100 = 50000 a a 2 = 50000 a = 100 槡 5 NH FM 100 槡 5 H F H F 1-2-85 2 H F H F 81
GFH FH = GF = HGF = 90 H = GH, H GFH F, F = H = HF = F F + F = = 90, F = + F = 90 Rt H Rt F H = 100 2 2 槡 + 200 = 100 槡 5 F = 100 2 2 槡 + 200 = 100 槡 5, H = F = = HF, FH F = 90, FH FH 思维拓展测试 1 2005 l 1-2-86 1 2 3 S 1 S 2 S 3 S 4 S 1 + S 2 + S 3 + S 4 = 3 1 2 S 1 S 2 S 3 S 4 l 1-2-86 2 2005 1-2-87 2 cm 4 槡 3 3 cm 2 82
H S 2 1-2-87 S 1 1-2-88 3 2005 1-2-88 2 S 1 S 2 S 1 S 2 S 1 > S 2 S 1 = S 2 S 1 < S 2 S 1 S 2 4 1-2-89 O F F H H H = 1 F 2 H F F O G H 1-2-89 1-2-90 5 1-2-90 F G H G F H 6 1-2-91 1 2 3 1 2 1-2-91 1 1-2-911 2 1-2-912 1-2-912 83
1-2-92 方法一 方法二 方法三 1-2-92 7 1-2-93 GF G F G 1-2-93 F P M 1-2-94 H F 1-2-95 8 1-2-94 M P P M PF M F 1 PMF 2 1 P PMF 9 1-2-95 4a FGH F G H H FG = FG FGH 答案与提示 1 4 S 1 + S 2 = 1 S 3 + S 4 = 3, S 1 + S 2 + S 3 + S 4 = 4 2 2 30 3 槡 3 H = 2 3 槡 3 H = 4 3 槡 3 H = 30, ' = 30 G 84
3 S 1 S 2 1 3 S 1 > S 2 4 F, F = F, = O = 1 2, = F O = O = 90 H HO = 90, OH, O = H, H = 1 2 = 1 2 F 5, = 90 = F = F = 45 F = F, F F, F = F Rt G H G, H = HG, GH = HG HG = GF GF + F = 90, HG = GH = GF HG + GF = GF + F = 90 FH = 90, F H 6 1-2-96 方法一 方法二 方法三 1-2-96 7 1-2-97 G M = FM M FM FM M FM F M FN N FMN 8 1 = 2 PMF M, M = 1 2 = 2, M = = N M M G 1-2-97 90, M = 45 M = 45, M = 90 PF M P M, PFM = PM = 90, PMF 2 P PMF P PF P = P, PMF 9 FGH, = = = = a = H, H = H = 85
, H = H, = H F = G H = FG, H = = G = F H FG = FG, F = HG FGH, = x = y = H = F = G = x H = G = F = = y = 90, H 2 = H 2 + 2 = x 2 + x 2, H = 槡 2x F = 槡 2y x + y = a, H + F = 槡 2 x + 槡 2 y = 槡 2 x + y = 槡 2 a FG + HG = 槡 2 a, H + F + FG + HG = 槡 2a + 槡 2a = 2 槡 2a FGH 2 槡 2a 视野情境扫描 1 1-2-98 O O 1 1 1 O 1 1 1 O O 1 4 1 1 1 F O 2 5 1 4 3 1-2-98 1-2-99 2 1-2-99 3 4 2 5 1 86
1 3 学习指导 4 ~ 10 1 2 3 1 2 知识点精析 1 1 2 1-3-1 2 1 上底 腰高腰 2 3 下底 1 1-3-1 2 87
3 4 1 2 4 1 1 2 2 5 1 2 3 6 1-3-2 1 S = 1 + 2 2 O 1S = S 2S O = S O 3S = S 问题探究 1-3-2 1-3-3 1-3-4 88
1-3-3 1-3-4 1-3-5 1-3-5 1-3-6 1-3-6 解题方法指导 1 1 2 1 2 3 1 2 1 2 3 1 2 1 2 89
2 1-3-7 = 70 = 40 = 6 cm = 15 cm 2 1 1-3-7 = 9 = 1 = = = 70, 1 = 70 = 40, 2 = 180-1 - = 70, 2 = 1 = 70, = = - = - = 9, = 9 cm 作什么样的辅助线一定要依题目条件和图形特征来确定, 没有固定模式 3 1-3-8 = = 3 cm = 5 cm 1-3-8 F 1-3-8 F F = = = F F F = 90 F F 90
= 1 2 F F F, F, F = F =, =, = F F, F, F F, F, = 1 F 2, = 1 2 + F = 1 2 + = 1 3 + 5 = 4 2, S = 1 2 + = 1 2 16 cm 2 4 3 + 5 = 16 4 2004 1-3-9 = = 1-3-9 91
= = = = =,, =, =, =, =, =,, =, 基础达标演练 1 = 55 = 78 = = 2 120 7 cm 13 cm 3 = 60 = = 4 cm = = S = 4 17 10 20 5 20 cm 60 4 cm 6 a = 16 cm b = 13 cm c = 10 cm d 7 2: 3: 3: 4 8 92
= 9 12 6 75 60 45 30 10 1-3-10 = 30 = 60 = 2 4 槡 3 3 槡 3 4 6 11 2005 1-3-11 = = 8 = 10 = 6 16 槡 15 16 槡 5 32 槡 15 16 槡 17 1-3-10 1-3-11 1-3-12 12 1-3-12 = = = 120 13 1-3-13 = 90 = 45 F F M F F = 14 2006 1-3-14 = F M 1-3-13 1-3-14 1-3-15 15 2005 1-3-15 = F = 2 F = 2F = F 16 2004 1-3-16 1 = 93
2 = 2 = 60 F 1-3-16 94 1-3-17 17 2005 1-3-17 = 90 = 2 F F F F 答案与提示 1 102 125 + = 180 + = 180 2 6 cm 3 2 cm 2 槡 3 cm 6 槡 3 cm 2 = 2 cm = = 2 槡 3 cm = S = 1 + 2 = 6 槡 3 cm 2 4 120 8 1 2 + = 1 10 + 20 8 = 120 2 5 4 cm 8 cm 20 6 7 cm < d < 13 cm 10 cm 16-13 = 3 cm 13 7 7 = 60 = = 90 = 120 8 9 6 12 45 10 = 90 = = 2 = = 2 = 4, = 6 11 F F = F = F = 6 Rt = 8 = 2 = 2 槡 15 S = 1 2 6 + 10 2 槡 15 = 16 槡 15
12 =, = = 120, = = 30, = = 30 =, = = 75, = 60 = 75 = 105 13 M F, M = M, M = = 45, M = 90 M = = 90, M, M = M = 90 - MF = M = 45, F = 90 - MF = 45, F = M, + F = M + M F = 14, = =, =,, =, 15 =, = = 2 F = 2F, = 2 3 F = 2 3, = F F, F, = F 16 1, =, =, =, = 2 = = = 60, = 30 = 90, = 2 = 2 = 4, 10 17 G G = = 90 G = 90, G, = G = 2, G = G, =, = F F, F 难点指津 1 1 2 3 3 95
2 1-3-18 F O O F, O= O = O = O, 3 = 4 F O O, O = 1 2 O= OF = 1 2 O, O = OF, 1 = 2 O O OF, 1 = 3, F, F, F O = OF O = O O = OF, O OF, = F, F 4 2 1 O 1-3-18 综合延伸 3 F 5 1-3-19 =2 1 2 = 60 = 2 S F 1-3-19 96
1 = 2 = = 1 2 = 1 = 2 2 F S F = 60 F = 槡 3 2 = 槡 3 1,, = = 1 2, = 1 = 2, = 1 2, =,, 2 F F = = 60,, F Rt F F = 1 2, F = 2 2 槡 - F = 槡 3, S = 1 2 = 1 = 2 + F = 1 2 2 + 4 槡 3 = 3 槡 3 97
6 1-3-20 mm 500 mm 300 mm 600 mm 250 mm 1-3-20 1 mm 2 1-3-20 2 1-3-21 1 2 300 250 500 1 1-3-21 600 2 1 500 300-100 + 300 200-100 + 300 150 = 10000 mm 2 2 1-3-22 1 4 10000 2 1-3-22 300 500 1-3-22 98
7 1-3-23 = 90 = 14 cm = 18 cm = 21 cm P 1 cm Q 2 cm P Q Q F t t 1-3-23 PQ PQ P Q P Q PQ PQ =, PQ P Q Q P PQ PQ = P = - P = 18 - t Q = 2t P PF F Q 1-3-23 Q QFP = Q = - Q = 21-2t, P = P - = t - 21-2t = 3t - 21 PQ, QF = 1 2 Q - P = 1 2 PQF, P = QF, 3t - 21 = 3 2 t - 9 t = 8 P 2t - 18 - t = 3 t - 9 2 t = 8 PQ 思维拓展测试 1 2005 1-3-24 = 60 = = 2 = 6 = 2 2004 99
M 1-3-24 N 1-3-25 3 2005 1-3-25 = = = 1 = 60 MN P MN P + P 4 = > = 13 槡 2 + = 34 24 22 20 5 1-3-26 = = = + = 180 = 6 2004 1-3-27 = = F F F 1 F = 2 F 1-3-26 1-3-27 100 1-3-28 7 2004 1-3-28 1 = 5 = 11 4 2 = a = b h c c = a b h
3 = 3 = 7 = 5 槡 2 8 2005 1-3-29 1 1: 1 2 M F N 1-3-29 1-3-30 9 2005 1-3-30 M N F M M 1 MNF 2 MNF 答案与提示 1 4 = = 2 = 4 2 = = = = 3 槡 3 MN MN MN P P + P = 60 = = 30 = 90 = 槡 3 P + P = 槡 3 4 = = 90 =, = 34 F F = 1 2, F = 17 Rt F F = 7, = 24 101 5 + = 180 + = 180 = + = 180 = = 90 = =
6 1 F = 2 =, = =, =, = F F, F = = 90 =, F, F = 7 1 F F = F = 5 = F = 3, = = 5, 26 2 c = a + b + 槡 a 2-2ab + b 2 + 4h 2 3 G G G = G = 5 槡 2 = G = 3, G = 10 2 + G 2 = 100 G 2 = 100, 2 + G 2 = G 2, G = 90 G G, 8 1 1: 1 1-3-31 2 1 2 1-3-31 1-3-31 9 1, = = M, M = M, M M, M = M F N M M, N = 1 2 M FN = 1 2 M M = 1 2 M MF = 1 2 M, N = FN = FM = M, NFM 2 M MN 1-3-32 M = M N = N, MN, MN, MN F MNF, M N N, MN = 1 2 1-3-32 视野情境扫描 102
J Fields 1863-1932 1924 1932 43 1500 1 4 学习指导 1 2 1 2 3 103
知识点精析 1 2 3 4 1 1 2 2 = 5 问题探究 1-4-1 1 1 2 2 5 5 5 1 2 3 4 5 1 5 2 2 3 4 5 1 P 5 5 1 2 3 4 5 P 1 3 3 5 5 1 1 104 1-4-1 1 2 3 4
2 2 4 4 3 3 1 1 5 5 3 3 2 5 5 4 4 解题方法指导 1 1 2005 1-4-2 16 cm FGH cm FGH cm 2 H G F F 1-4-2 1-4-3 2 2005 1-4-3 F S F = 2 4 6 8 12 1 F G H F F = 1 2 HG = 1 2 H = 1 2 FG = 1 2 F = FG = HG = H = 1 2 = = 4 105
= 4 槡 2, F = 2 槡 2 FGH 4 2 槡 2 = 8 槡 2 F = FG = HG = H 1 FGH G HF = HF = 4 FGH 2 G HF = 8 cm 2 2 F S F = S F = 2 S = S F = S F = 2 4 2 = 8 1 8 槡 2 8 2 1 2 2 1-4-4 > 1 2 = 1-2 F 1-4-4 F F 1 F, = F = 90 = F =, F, = F F = =, F 2 = F =, = 1 F 2, = 1 2 - F = 1-2 106
3 1-4-5 = M P N MN Q P Q P M N Q 21 G 1-4-5 P = Q PQ = QP M N = MG NG P = Q G MG NG N G, GN = 1 2 MG = 1 2 =, GN = MG, 1 = 2 MG, 2 = QP NG, 1 = PQ, PQ = QP, P = Q 4 2005 1-4-6 F 6 5 11 16 17 22 1-4-6 F 107
F = 6 + = 12 = = 5 12 + 10 = 22 5 1-4-7 = cm 20 1-4-7 + =, =, =, =, = = = 1 2, = = = 1 2, = 30, = 1 2 30 = x = = = x = 2x, x + x + x + 2x = 20 x = 4 +, = 4 = 8, = 6 cm 2 基础达标演练 1 60 cm 2 3 2: 3 20 cm 108
4 Rt = 90 F = 4 cm = 6 cm F 5 1-4-8 F F = 2 = 6 1-4-9 = 5 cm = 12 cm cm F 1-4-8 1-4-9 1-4-10 7 1-4-10 = 120 = 2a 8 2005 9 2005 1-4-11 F O FO - O = 3-4 6 8 10 10 2004 1-4-12 = 90 18 cm 9 2 cm 9 cm 12 cm 18 cm F O F G 1-4-11 1-4-12 109 1-4-13 11 1-4-13 = F G = 20 = 66 FG
110 47 48 41 23 12 1-4-14 = 40 = 50 M F N F = a MN = b a + b a + 2b 2a + b 2a - b 13 2004 1-4-15 O = F OF = 1 2 F N M 1-4-14 F 1-4-15 O Q P M N 1-4-16 14 1-4-16 M N P Q MNPQ 15 1-4-17 G G G G F G P M P F = 1 P 2 16 1-4-18 F GH = G = G = 18 = 32 F + GH M F G P 1-4-17 G 1-4-18 F H H G F 1-4-19 17 1-4-19 = F F H G H G 答案与提示 1 40 cm 2
3 16 cm 24 cm 2k 3k 1 2k + 3k = 20 2 k = 8 2k = 16 3k = 24 4 2 cm 3 cm F = 90 F F = 1 = 3 cm 2 = 1 = 2 cm 2 5 2 F F = =, = = = 2 6 6 5 = 90 = = 5 = 12 = 13 = + = + 1 + = 2 13 2 = 6 5 6 5 cm 3 7 2 a = 30 = 90 = 1 = a 2 1 = = a 2 a + 2a = 3 2 a 8 9 F F O, O = 1 2 OF = 1 2 1 - = OF - O - = 6 2 10 = 1 = 3 2 1 2 + = 9 2 1 2 11 FG G FG 1 = 2 G = = FG = G = 20 = 66 GF = 134 G = GF FG = 1 180-134 = 23 2 111 12 N NH NG H G GNH = 90 MN Rt GNH MN = 1 2 GH = 1 - = b, - = 2 2b F, + = 2a = a + b 13, = =, F =
F F = F, F F, F = F O = O, OF = 1 2 14 P N, PN = 1 2 QM =, MNPQ 1 2, QM = PN 15 M P, M = 1 2 P, MF = GP FG PG FG PG, GF = GP FM = PF, MF = FM, M = F, F = 1 2 P 16 F GH = G = G, F = FH = H, F GH GH F = 18 = 32, 18 + GH = 2F + 32 = 2GH, F + GH = 50 17 M FM M F = F M = M, FM = = M = M, M = 1 2 1 2 =, FM = M MF = MF M, MF = G FM,, H = G 难点指津 MF = H 1-4-20 O F F = 1-2 F G G, G = 1 2 FG, FG = 1 2 112 H O F 1-4-20 G
, F = G - FG = 1-2 F G G F G F H G G G F G F G 综合延伸 6 1-4-21 = O O = 60 F G F O O O FG O G 1-4-21 F = 1 2 = G FG O = 60 O = O O O O = 90 G G = 1 2 FG = 1 2, = =, =, O 113
O = O = 60, O O, O = 90 Rt G, G = 1 2 FG = 1 2 Rt O F O O, F = 1 2 = 1 2 = G = FG FG 7 1-4-22 = a 1 1 1 = 1 2 = 1 2 a 2 2 1 1 ( ) 2 2 = 1 1 1 2 1 1 + = 1 1 2 2 a + a = 3 4 a 2 2 3 3 3 3 2 2 3 3 = 1 2 2 2 + = 1 3 1-4-22 2 ( 4 a + a ) = 7 8 a n n n - 1 n - 1 n n n 1 n n n n = 1 1 1 = 1 2 a = 21-1 a 2 1 n = 2 2 2 = 3 4 a = 22-1 a 2 2 n = 3 3 3 = 7 8 a = 23-1 a 2 3 n n = 2n - 1 2 n a 114 1
1 2 3 思维拓展测试 1 1-4-23 ' ' F =3 cm F =4 cm ' + ' = 2 100 cm 20 cm 2 S GF 3 1-4-24 F G =2 槡 2 cm 2 cm 2 1-4-23 F G 1-4-24 115 F 1 2 3 1 cm 1 3 2 3 2 3 2 1-4-25 4 2004 1-4-25 a 2 1 1 1 1 1 1 1 1 2 2 2 2 n n n n n n n n 5 F 2F + 2F = + 2F > + 2F < + 1 6 1-4-26 R P F P RP P R F F F F 7 1-4-27 = F G O OF = 2OF
R F P 1-4-26 1-4-27 1-4-28 8 1-4-28 F G H G HF 9 2004 =10 1 1-4-29 1 2 1-4-29 2 1 2 1 2 1 2 1 1 + 2 2 3 1-4-29 3 1 2 10 1 2 10 1 1 + 2 2 + + 10 10 1-4-29 10 1-4-30 = 6 = 8 1 1 1 1 1 1 1 1 2 2 2 2 n n n n 1 1 1 1 1 2 2 2 2 2 3 1 1 1 1 2 2 2 2 4 n n n n 答案与提示 1-4-30 116
4 = 1 2 1 2 F F = 1 + 2 +3 =5 cm ' + ' = - '' = - =5-3 =2 cm 1 2 500 + +2 = 100 2 + 25 =500 cm 2 3 8 槡 2 h S GF = 1 2 F 1 2 h = 2 槡 2 F h =8 槡 2 cm 2 a 2 4 S 2 n 1 1 1 1 = 1 2 a2 S 2 2 2 2 = 1 2 2 a2 1 n n n n 2 n a2 5 G FG G GF + G > F FG= 1 2 G= 1 2, G+ FG= 1 +, G+ FG>2F 2 6 P P PR F R F PR F F = 1 2 R 7, = O = O =, =,, F = F O = O, =2OF 8 G HF H FG GH H, H = 1 2 G F, GF = 1 2, H GF H = GF, FGH, HF G 117 9 1 = 1 =5 2 2 1 1 = x 2 2 =2x 1 2 1 1 2 2 x +10 =4x x = 10 3 1 1 + 2 2 =10 3 1 1 + 2 2 + 3 3 = 15 1 1 + 2 2 + 3 3 + 4 4 = 20 1 1 + 2 2 + + 10 10 =50
10 1 1 1, 1 1, 1 1 1 1 = 1 2 1 1 1 1 = 1 2, 1 1 1 1 1 1 = 1 1, 1 1 1 1 1 1 1 1, 1 1 1 1, 1 =90, 1 1 1 1 2 2 2 2 2 3 S = 1 2 6 8 = 24, S 1 1 1 1 = 1 2 24 = 12, 1 1 1 1 12 2 2 2 2 6 1 4 n n n n 2 24 n 视野情境扫描 1607 15 3 1606 1607 5 1852 118
1 5 学习指导 知识点精析 1 1 2 3 2 1 2 3 问题探究 119
120 解题方法指导 1 60 60 60 60 60 60 2
= =90 + + =90 +90 + > 180 3 1-5-1 F P F 121 1-5-1 F F F, F F, F, F 1-5-2 F F F P, P F, F, F
基础达标演练 1 F F F F h F h F 2 1-5-2 3 1-5-2 4 a + b > 0 a > 0 b > 0 a > - b > 0 b > - a > 0 a > b > 0 b > a > 0 a b 5 1-5-3 P 1 P P P 1 2 1-5-3 1 2 3 1-5-4 6 1 3 1-5-4 1 1 1 2 2 3 3 4 答案与提示 122
1 h F 2 = = 3 4 a 0 b 0 a + b 0 5 P P P 1 2 P 1 2 P 1 2 P 1 2 P + P 1 P P + P >, < 1 = = = 1 1 6 1 1 2 2 3 3 4 1 > 1 4 1 2 > 1 4 2 3 > 1 4 3 > 1 4, 1 + 1 2 + 2 3 + 3 > 1 4 4 = 1 1 > 1 4 难点指津 1 2 3 4 综合延伸 123
124
4 n 5 O 5 6 1-5-5 F 6 O O< O < O O O > 60 1-5-5 O > 60 O > 60 O > 60 OF > 60 FO> 60, O + O + O + O + OF + FO> 360 O + O + O + O + OF + FO= 360 5 5 y = x 2 - m - 3 x - m m x x x x x 1 + x 2 > 0 x 1 x 2 > 0 m - 3 > 0 - m > 0 m 抛物线与 x 轴的两个交点的横坐标就是关于 x 的一元二次方程的两个根, 你还记得吗 125
126 m x x 思维拓展测试 1 2005 1 2 3 2 1-5-6 3 P P < P 4 1-5-6 5 1 2 答案与提示 1 2, 3 P 1 P 1-5-7 1 P > P < P 2 P 1-5-7 2 P P > >, P > P <, P 1 2 P P
1-5-7 4 3 4 3 = 6 2 0 1 2 3 5 = 6-1 4 = 6-2 5 4 3 0 1 6 3 = 6-1 3 3 1 2 0 = 6-2 3 0 1 5 1 2 1-5-8 1-5-8 RQP RQP 2 R P S S = 1 2 S QP S S = 1 2 S R S = S + S 1 2 S QP + 1 2 S R = 1 2 S RQP < 2 1 = 1 2 S = 1 1-5-8 1 2 视野情境扫描 L Lemhus 1840-1-5-9 = = 127
1-5-9 1-5-10 1-5-10 ' ' ' ' ' ' ' ' = ' ' = ' ' 1 = 2 < > < < = 1 2 < 1 = 2 ' ' ' = = + > + = = ' ' ' ' ' ' > ' ' ' 1 = 2 3 > 4 ' ' > ' ' > = = < < 1 2 < 1 2 < > < < > = 100 20 80 2000 80 128
1 6 学习指导 知识点精析 1 1 2 3 2 1 2 3 2 O O 解题方法指导 1 O 1 2 1 129
2 1-6-1 1-6-1 2 1-6-2 1-6-2 1 O 2 O 1-6-3 基础达标演练 1-6-3 1 O 1 2 3 4 2 3 1-6-4 130
1-6-4 1-6-5 4 1-6-5 答案与提示 1 1-6-6 1-6-6 2 3 1 1-6-7 1 2 3 1-6-7 2 2 O O 1-6-7 4 1-6-8 1-6-8 131
视野情境扫描 1-6-9 1-6-9 O 1-6-9 132
热点题型分析 1 1 2005 2 2005 1-7-1 = 1 P P P 1-7-1 3 2005 6 8 1 2 4 3 7 = 6 + 8 = 7 2 2 2005 1-7-2 F = F = F 1-7-2 F F F, =, = F F 133
{ = = F = F, F, = F 3 2005 1-7-3 = F 1 F 2 = 12 cm F 1-7-3 1 F = 1 2 F = 1 2 = 2 1 F, F, F = 1 2 F = 1 2 =, = F, F 2 = 12 cm F, F = 6 cm, F 4 6 = 24 cm 4 2005 1-7-4 = 90 F F = 1 2 F 1-7-4 134
F F F = F = F, F, F F > = 1 2, F, F = 1 2 F = 1 2, = F, = = F = 90 = 90 =, F, = F =, = F, F 热点考题训练 1 2005 1-7-5 = 50 = 2 2005 1-7-6 1-7-5 1-7-6 1-7-7 135
3 2005 1-7-7 4 1 + 2 + 3 = 4 2005 1-7-8 20 2 5 2006 100 6 2005 1-7-9 = 8 cm = 6 cm cm 1-7-8 1-7-9 1-7-10 7 2005 6 = 60 P P = P = 2 槡 3 P 8 2004 1-7-10 = 3 = 2 F F = 2F F 9 2004 M M M 48 cm cm 2 10 2004 1-7-11 1 2 2' 1 64 cm 7 cm 1-7-11 1-7-12 11 2004 1 O 12 2004 1-7-12 8 M 136
M = 2 N N + MN 13 2005 14 2005 15 2005 16 2005 17 2005 90 3 7 2 3 4 5 18 2006 1-7-13 2 FG F S S = 2 S = 2 4 S = 4 S F G 1-7-13 1-7-14 1-7-15 19 2005 1-7-14 = 2 O F O O O O O O O O FO 20 2005 1-7-15 137
O O = 6 cm O 6 cm 4 cm 3 cm 2 cm 21 2005 22 2005 1-7-16 F G H S 1 S 2 S 1 > S 2 S 1 < S 2 S 1 = S 2 F 1-7-16 1 138 1-7-17 2 23 2006 1-7-17 1 4 F 1-7-17 2 2 4 8 10 24 2005 1-7-18 O O 1 O = 槡 3 = 1 1 ( ) 3 ( ) 槡 3 2 3 2 2 槡 3 2 ( ) 1 ( ) 槡 3 2 3 2 槡 3 2 1-7-18 25 2006 1-7-19 F = F F 26 2005 1-7-20 O O
F 1-7-19 1-7-20 1-7-21 27 2005 1-7-21 O O F F O = OF 28 2005 1-7-22 = 90 F F = F 29 2005 1-7-23 F F = 1 2 G F H GH 1-7-22 1-7-23 1-7-24 30 2005 1-7-24 1 cm F 1 = F 2 31 2005 1-7-25 = 60 = F = F F P PF 1-7-25 32 2006 1-7-26 FG Rt 1-7-26 = 2 = 60 Rt FG F ' ' ' ' ' ' 1-7-26 139
1 ' ' ' 2 ' ' ' F 0 1 G G F F 答案与提示 1-7-26 1 50 = = 50 2 1-7-27 1-7-27 3 135 2 = 45 1 + 3 = 90, 1 + 2 + 3 = 135 4 20 槡 3 1-7-28 O = 60 O = 90 O = 30 O= 1 2 = 1 20 = 10 2, O= 1 2 O O = 20 = 槡 O 2 - O 2 = 槡 20 2-10 2 = 10 槡 3 2 10 槡 3 = 20 槡 3 140 1-7-28 5 100 80 100 80 80 6 24 5 F F = = 8 cm = 90 = 10 cm S = 1 2 = 1 2 F F = 24 5 24 5 cm
7 2 槡 3 4 槡 3 P, = = 60, = = P = P, P P = 2 槡 3 P P = 4 槡 3 8 2 F = 2 = 1 F = - - F = 6-3 - 1 = 2 9 128 M M M = M M = 90, M = M = 45, M =, = 2 + = 24, = 8 = 16, S = 16 8 = 128 10 8 2' + 2 = 64 2, 2 = 642 2 3 = 642 2 7 = 642 2 2, 7 64, 7 6 8 11 槡 2 1 2 = 槡 2 2 = 1 槡 2 2 1 12 10 M N N + MN M M 10 13 14 15 16 17 4 2 18 F F S F = S = 2 19 20 O 21 22 FGH S = 141
1 2 G FH S = G FH 23 24 O = 槡 3 = 1 O = 2 O = 90, O = 30, 1 O = 30 1 O = 30 1 1 y 1 = 1 2 O 1 = 1 2 O = 槡 3 2 O = 3 2 1 ( ) 槡 3 2 3 2 25, = = = F, F 26, O = O =, O, O 27, O = O, O = FO O = OF, O OF, O = OF 28, = 90, = 1 2 = = F =, F =, F, F 29 1 F F 2 1-7-29 F =, F + F = + F = F, H G, = =, F, = F, H G, GH 30 1 F, F = = 90, = F =, Rt Rt F, = F = F Rt F F = 45, F = F, = F 2 1 cm = 1-7-29 槡 2 cm 1 = F = - F = - = 槡 2-1 cm 31 PF = 120 = = = = F = F, F, = F = 120, F + F = 60, F + = 60, P = 120, PF = 120 142
32 1 30 ' ' ' Rt FG F, F = ' ' = 60, ' F, ' F = 60, ' = 30 2 'F ' F 槡 3 = 30 = 60, = 90, = 1 2 = 1 = 槡 3 Rt ' ' = 90 ' = 60, ' = 30 ' = 2 - 槡 3, ' = 4-2 槡 3 = 2 槡 3-3, S F = S ' F - S ' = 6-5 2 槡 3 2 7 100 120 3 30 1 4: 9 78 cm cm cm 2 45 3 10 cm 4 45 4 1: 5 1 5 cm 5 1-8-1 = 4 cm : = 2: 1 = 1-8-1 143 1-8-2 6 1-8-2 = 5 = 8 F F = 7 1-8-3 P = 4 M M P PF
1-8-3 144 1-8-4 8 1-8-4 O F = 12 O: OF = 1: 2 = 9 10 > = 2 = a = b 3 30 11 1-8-5 = 1 2 O = 4 cm O 12 4 cm 3 cm 2 槡 3 cm 4 槡 3 cm 1-8-5 13 1-8-6 = 30 = 2 3 2 槡 2 槡 6 槡 7 14 1-8-6 15 2 S 槡 S 1 2 槡 S 1 2 槡 3S 1 2 槡 5S 16
= = 17 40 30 60 50 40 30 18 O O G O O = OG G G = G G G = G 19 1-8-7 F F 64 F 50 20 24 25 26 1-8-7 1-8-8 20 1-8-8 = 30 = 60 = 2 6 2 槡 3 4 槡 3 4 60 21 10 1-8-9 F G F H HFG 1-8-9 1-8-10 22 10 1-8-10 = 20 cm 23 10 1-8-11 F 145
F = 40 m F = 30 m F 24 15 1-8-12 Rt = F O F = 2 1 = 槡 2 2 = 2 槡 2-1 F 1-8-11 1-8-12 1-8-13 25 15 1-8-13 F F F 1 1 F 2 2 F 答案与提示 1 12 27 4x cm 9x cm 4x cm 9x cm 4x + 9x + 4x + 9x = 78 x = 3 12 cm 27 cm 2 22 5 67 5 3 32 cm 2 6 cm 4 12 cm 30 150, 30 2 3 cm, 4 3 = 12 cm 5 8 3 槡 3 cm, = 90 : = 2: 1, = 30 = 90, = = 2 = 4, = 8 3 槡 3 = 8 3 槡 3 6 2 = = 5 = = 8 146, = =, =, = = F, F = + F - = + - = 5 + 5-8 = 2
7 4 S P = S PF, S M = 1 4 S = 1 4 4 4 = 4 8 16 O: OF = 1: 2 F = 12, OF = 8, = 2OF = 16 9 90 10 a + b 1-8-14, = = b = = a = = 2 = + = 2,, = + = + = a + b =, = = a 11, + 147 1-8-14 = 180 = 1, = 60 2, = 90 - = 30, = 2 = 8 cm = = 4 槡 3 cm O= O, O = 1 2 = 2 槡 3 cm 槡 2-12 1-8-15 = + = 180, + = 180, 13 Rt = 30 = 2, = 1 2 = 1 = 2 2 槡 - = 槡 3 2 = 槡 8 2-4 1-8-15, = 2 = 2, Rt = 槡 2 + 2 = 槡 3 2 + 2 槡 2 = 槡 7 14 ( ) 15 2x x 2 x + 2 S = 1 2 x 2x = x2 = S x = 槡 S, 槡 5 2 5 槡 S = 槡 S 2 槡 2 = 槡 5 2 x 16 17 10 5 2
18 O = O = O, O = OG = 90 O = OG, O OG, = G O = OG Rt O O + O = 90, OG + O = 90, G 19, = = = 90 S = 2 = 64 = 8 F = = 90 F =, F, = F S F = 1 2 2 = 50 = 10 = 8, Rt = 槡 2-2 = 6 S = 1 2 6 8 = 24 20 120 30 = 2 槡 3 = 6 F Rt F Rt F F = 1 = 1 F = + F = 3 = 2F = 6 2 148 21 F G HF G FH G = HF 22, =, =, =, = =, =, + = 90, 3 = 90, = 30, = 1 2 = = = x = 2x, 5x = 20 x = 4, = 4 = 8 1, 4 + 8 = 6 cm 2 23 F,, OF = O F, O = O OF = O = 90, OF O, OF =, F F, F, S F = 1 2 F = 1 2 30 40 = 600 2 24 1 = 2, = 2 F, = = = x = - = 2 - x Rt 2 + 2 = 2
2 - x 2 + 槡 2 2 = x 2 x = 3 2, = 3 2 2 G G G = - = 2-2 槡 2-1 = 4-2 槡 2 G 2 + G 2 = 2 G = G, 2G 2 = 2 = 4-2 槡 2 2, G = 槡 2 2 4-2 槡 2 = 2 槡 2-2, = G G, O = FO O = OF = 90 O = O, O OF, = F F, = F = F, = = F = F, F 25 1 = 1 2 F F, F, = F,, =, = = F = 1 2 F =, = 1 2 F 2 F 1 =, = = F, F = F + + F + F = 180, 2 F + = 180, F + = 90, F = 90 F 149
2 1 学习指导 知识点精析 1 2 k k 360 360 148
问题探究 2-1-1 2-1-1 1 2 3 2-1-2 2-1-3 2-1-2 2-1-3 k 360 149
解题方法指导 1 1 2-1-4 1 60 2 2-1-4 2 2-1-4 1 60 60 60 120 120 120 3 = 360 60 6 = 360 120 2 + 60 2 = 360 2 1 2-1-5 1 2-1-5 2 认真观察瓷砖铺设的图案, 为后面的图案设计作好准备 2-1-5 60 2-1-6 1 2 150
2-1-6 2 2005 2-1-7 2-1-7 90 135 135 135 360 3 2-1-8 8 151 2-1-8 60 cm 2 x cm y cm x + y = 60 { 2x = x + 3y x = 45 { y = 15 45 cm 15 cm
4 2-1-9 1 2-1-10 2 2-1-9 2-1-10 1 360 2 5-2 180 1 = 108 3 2 108 < 360 < 4 108 108 2 2-1-11 2-1-11 152
基础达标演练 1 2-1-12 2-1-12 2-1-13 2 2-1-13 3 4 7 2-14 X X 2-1-14 5 2-1-15 3 3 180 150 120 90 2-1-15 2-1-16 6 2-1-16 153
7 8 2-1-17 2-1-17 2-1-18 9 2-1-18 1 2 3 10 2-1-19 答案与提示 1 16 2-1-19 2 27 3 360 4 2-1-20 154 2-1-20 5 360 3 = 120 6 12-2 180 7 = 150 360 = 2 4 12 150 8 α 3α = 360, α = 120 180-120 = 60, 120 120 60 60
9 1 2-1-21 2-1-21 2 2-1-22 2-1-22 3 2-1-23 2-1-23 10 2-1-24 2-1-24 难点指津 1 155
2 综合延伸 5 2-1-25 1 30 cm 20 cm F G H 4 2 m 2 8 m 1 2 2-1-25 1 = 2 2-1-25 2 4 + 4 4 2 m 2 8 m 30 cm 20 cm 13 13 1 4 2 2 8 = 11 76 m 2 0 3 0 2 = 0 06 m 2, 11 76 0 06 = 196 2 4, 4 2 m 2 8 m 30 cm 20 cm 13 13 13 13 = 169 156
196 169 + 196 = 365 6 2005 2-1-26 2-1-27 2 3 2-1- 28 2-1-26 2-1-27 2 45 135 1 3 6 2 5 4 45 135 3 4 1 3 6 1 2 6 1 5 6 2-1-28 2-1-28 157
思维拓展测试 1 2005 2-1-29 12 2 2005 2-1-30 n 2-1-29 2-1-30 3 1 2 2-1-31 1 2 1 2-1-31 2 3 2 2-1-31 3 n n n 2-1-31 4 2-1-32 0 1 2 3 2-1-32 158
5 I 2-1-33 7 2-1-33 2-1-34 6 2-1-34 2 cm 2-1-34 1 cm 1 cm 1 2 3 2-1-35 2-1-36 2-1-37 4 5 2-1-38 2-1-39 6 2-1-40 159
答案与提示 1 1: 2 60 60 120 120 60 2 5n + 3 8 8 + 1 5 8 + 2 5 8 + 3 5 8 + n - 1 5 n 8 + n - 1 5 = 5n + 3 3 8n - 6 n 1 2 2 10 3 18 8 n 8n - 6 4 5 I a b i H h = x e = 7 F I G f = 7 + x i = 7 + 2x g = 7 + 3x d = 4x c = 7 + 7x a = 7 + 11x b = a + d - e = 15x b = e + f = 14 + x 15x = 14 + x x = 1, a = 18 b = 15 c = 14 d = 4 g = 10 i = 9 f = 8 6 2-1-41 2-1-41 视野情境扫描 2-1-42 160
3 2-1-42 2-1-42 2-1-43 2-1-44 3 2-1-43 2-1-44 3 2 2 学习指导 1 2 知识点精析 1 1 161
1 2 n n n 3 n 4 3 2 3 1 2-2-1 n n - 3 n n n - 3 2-2-1 2 2 n n - 2 2 2-2-2 2-2- 3 2-2-2 162 2-2-3
3 1 n n - 2 180 2 360 n 360 问题探究 1 2-2-4 1 1 3 1 4 1 5 1 n - 1 n 1 2 3 n n - 2 180 n n - 2 180 2 P 2-2-4 2 n n - 1 n - 1 n - 180 P n n - 1 180-180 = n - 2 180 2-2-4 3 O 2-2-4 3 n n n n 180 O n n 180-360 = n - 2 180 180 360 n 180 n 180 163
n 180 - n - 2 180 = n 180 - n 180 + 360 = 360 解题方法指导 1 1 2005 2 2005 540 1 6-2 180 = 720 720 = 120 2 6 n n - 2 180 = 540 n = 5 1 120 2 1 n n - 2 180 2 n 2 9: 2 n - 2 180 360 n n - 2 180 360 n - 2 180 : 360 = 9: 2 n - : 2 = 9: 2 n = 11 164
3 1800 m n m - 2 180 + n - 2 180 = 1800 m n m n m - 2 180 + n - 2 180 = 1800 m + n = 14 m n 2 14 m = 10, { n = 4 { m = 8 n = 6 { m = 6 n = 8 m = 4 { n = 10 4 2-2-5 1 = 2 = 135 = 100 = 2-2-5 NM MN MN 1 = 2 1 = 2 1 = MN 165
, 2 = MN,, MN + MN = 180 NM 5-2 180 = 540, = 540 - - - MN - MN = 540-135 - 100-180 = 125 5 2-2-6 + + + = 140 1 + 2 + 3 2-2-6 1 = + 4 4 = +, 1 = + + 3 = 5 + 5 = +, 3 = + + 2 + + = 180, 2 = 180 - - 2 1 3, 1 + 2 + 3 = + + + + + + 180 - - = 180 + + + + + + + = 140, 1 + 2 + 3 = 180 + 140 = 320 1 + 2 + 3 + 6 + 7 = 5-2 180, 1 + 2 + 3 = 540-6 + 7 166 = 540
6 + + = 180, 6 = 180 - - 7 + + = 180, 7 = 180 - -, 6 + 7 = 180 - - + 180 - - = 360 - + + + + + + = 140, 6 + 7 = 360-140 = 220, 1 + 2 + 3 = 540-220 = 320 基础达标演练 1 2004 n 150 n = 2 2005 72 3 14 4 2160 5 n 7: 2 1 6 5 7 1800 540 720 810 8 1 2 3 4 5 1 2 3 4 9 10 20 30 80 6 7 8 9 10 120 5 4 3 2 167
11 2880 140 150 160 170 12 1: 2 3: 8 4 8 5 10 6 12 7 4 13 150 14 n 90 n 15 2-2-7 F F 16 2-2-8 + + + + + F 2-2-7 2-2-8 答案与提示 n - 2 180 1 12 n = 150 n = 12 n 2 5 360 72 = 5 3 5 7 n n - 3, n = 5 2 n n - 3 5 = 14 n = 7 2 4 12 n - 2 180 + 360 = 2160 n = 12 5 9 n - 2 180 : 360 = 7: 2 n = 9 6 12 1800 360 α β α + β = 180 β = 1 5 α β = 30 360 30 = 12 12-2 180 = 1800 7 n - 2 180 180 8 2 5 168
9 10 20 30 80 8 8 n - 2 180 10 120 = n 120 n = 6 n - 3 3 11 n - 2 180 = 2880 n = 18 2880 18 = 160 12 n 1 n 2 n 1-2 180 : n 2-2 180 = 3: 8 n 1 : n 2 = 1: 2 n 1 = 5 n 2 = 10 13 n n - 2 180 = n 150 n = 12 12-2 180 = 1800 1800 14 x x - 90, x + x - 90 = 180 360 x = 135 n 135 n = 180-135 = 8 15 = = = = 108, = = 36 = = 36, - = 108-36 = 72, F = 72 108 F 72 16 G F M F = 180 - - = G G = + GM + G = GMF, GMF = + + FM + + F + GMF = 360, + + + + + F = 360 难点指津 1 360 n 169
360 3 360 n n 3 2 n n - 1 n + 1 n 2-2-9 1 2 3 综合延伸 2-2-9 6 1680 1 n n 3 2 0 180 3 n n - 2 180 180 180 n x n - 2 180 = 1680 + x, n - 2 = 9 + 60 + x 180 n = 11 + 60 + x 180 n, 60 + x 180 0 < x < 180 170
, x = 120 n = 12 12 120 n 1680 < n - 2 180 < 1680 + 180 11 1 3 < n < 12 1 3 n, n = 12, n - 2 180-1680 = 120 12 120 180 180 7 2004 2 3 4 2-2-10 2-2-10 2-2-11 n 2-2-11 171
n 2-2-12 2-2-12 14 25 36 n n - 2 n - 1 n 思维拓展测试 1 6 1 2 1 10 3 n n 4 n 40 5 16 15 16 17 16 17 15 17 16 17 18 6 1125 7 120 125 5 63: 8 8 172
100 140 9 2-2-13 = 60 = 135 F F = 105 F = 30 1 F 2 2-2-13 173 2-2-14 10 2-2-14 30 20 答案与提示 1 20 n - 3 n n - 3 n - 2 n - 2 = 6 n = 8 n = 8 20 2 1 2 12 1 180 n - 2 10 180 = 180 n = 12 3 5 n 3 n 3 n 3 + 2 = 5 360 4 n 40 n 9 5 1 6 n x 0 < x < 180 n - 2 180 = 1125 + x x = 180 n - 1485 0 < x < 180 n, n = 9 x = 135 135 7 n n - 2 180 120 + n - 1 5 n - 2 180 120 + n - 1 5 = 63 8 n = 9
, 9 8 n 100 + 140, = 120 2 n - 2 180 = 120 n n = 6, 9 1 F F = 105 F = 30, F = 180 - F - F = 180-105 - 30 = 45 2 F F = 45 = 135 = 60, = 360 - F - - = 360-45 - 135-60 = 120, + = 120 + 60 = 180, 10 2-2-15 F = 20 F = 30, + = 180-20 = 160 + = 180-30 = 150 + = 160 + = 150 视野情境扫描 2-2-15 1 n 2 n 2-2-16 1 5 n n - 2 2-2-16 174
n n N N = n - 2 N 180 = n - 2 180 2 L uler 1707 ~ 1783 1751 Goldbach 1690 ~ 1764 n n n 3 = 1 4 = 2 5 = 5 6 = 14 7 = 42 8 = 132 9 = 429 2-2-17 14 2-2-17 J Segner 1704 ~ 1777 1758 n = 2 n - 1 + 3 n - 2 + + n - 1 n 2 6 10 4n - 10 n = n - 1 1941 H Urban n + 1 = 4n - 6 n n 175
2 3 学习指导 1 2 知识点精析 360 1 n k n n - 2 k 180 n = 360 n - 2 k - 2 = 4 kn - 2k - 2n = 0 n = 2k k - 2 = 2 + 4 k - 2 4 n k, k - 2 176
, k = 3 n = 2 + 4 3-2 = 6 k = 4 n = 2 + 4 4-2 = 4 k = 6 n = 2 + 4 6-2 = 3 1 3 6 2 4 4 3 6 3 2 m x n y m n m m - 2 m 180 n n - 2 n 180 x m - 2 180 + y m n - 2 n 180 = 360 x + y - 2 mn - 2 nx + my = 0 m 3 1 y 1 m n x y 177 n 3 m n x m n x y x y
3 4 6 8 12 1 3 2 2 4 1 3 2 2 4 1 2 5 1 2 问题探究 60 90 108 120 135 1 2 178
360 60 = 6 360 90 = 4 360 108 = 3 2 9 360 120 = 3 360 135 = 2 2 3 3 60 + 2 90 = 360 4 60 + 1 120 = 360 2 60 + 2 120 = 360 1 90 + 2 135 = 360, 解题方法指导 360 1 2005 124 234 134 123 1 60 6 2 90 4 4 3 3 108 360 179 360
180
2 2005 2-3-1 n 2-3-1 1 6 2 6 + 1 4 3 6 + 2 4 n 6 + n - 1 4 = 4n + 2 4n + 2 360 3 2005 120 60 90 m n 120m + 90n = 360 4m + 3n = 12 m n, 181
4 1 2 1 60 150 150 2 + 60 = 360 360 2 90 135 2 + 90 = 360 1 2-3-2 2-3-2 2-3-3 2 2-3-3 360 360 1 x y 60x + 150y = 360 2x + 5y = 12 x = 5 6-2 y x y y = 2 x = 1 5 2-3-4 2-3-4 182
1 2 1 1 2 3 2 基础达标演练 1 2 3 4 2-3-5 2-3-5 1 1 2 2 3 3 4 4 5 5 5 2004 獉獉獉 6 183
7 8 3 4 答案与提示 3 4 8 4 6 4 3 6 1 3 2 3 3 2 60 3 + 90 2 = 360 4 1 2 3 4 5 5 135 360 135 6 m n 90 m + 120 n = 360 3m + 4n = 12, m = 4-4 3 n n 3 6 9 m m = 0-8, m 7 150 360 150 = 2 4 8 90 + 90 + 60 + 120 = 360 难点指津 1 2 184
综合延伸 6 m n m n m n m n 60m + 120n = 360 m n m n m n 60 120, 60m + 120n = 360 m + 2n = 6, m = 6-2n m n, n = 1 m = 4 m = 2 n = 2 m n 4 1 2 2 1 360 2 7 1 1 60 90 60 90 120 150 60 90 60 120 150 n - 2 180 = 11-2 180 = 1620 120 11 < 1620 < 150 11, 120 150 120 x 150 y 120 x + 150 y = 11-2 180 1 x + y = 11 1 2 { x = 1 y = 10 2 185 2-3-6
, 1 120 10 150 2-3-6 186
8 2003 2 2-3-7 8 2-3-7 a = 思维拓展测试 1 a b b = 2 3 2004 8 4 5 6 8 4 2005 187
5 n n + 76 n n 6 2-3-8 2-3-8 1 n n 2 y y 1 n n 3 506 n 4 4 3 3 5 7 6 m 3 5 m 40 40 cm 2 30 30 cm 2 50 50 cm 2 60 60 cm 2 答案与提示 1 1 2 60a + 150b = 360 2a + 5b = 12 a = 6 - b = 2 a a = 1 188 5 2 b 2 6 60 90 120 60 3 + 90 2 = 360 60 2 + 120 2 = 360 + 90 2 + 120 = 360 6 3 x 135 + 135 + x = 360 x = 90
4 5 a b a 2 n = b 2 n + 76 n a + b a - b = 2 2 19 b 2 1 n a b a + b > a - b a - b = 1 a + b = 19 n = 4b 2 a = 10 b = 9 n = 324 6 1 n + 3 n + 2 2 y = n + 3 n + 2 = n 2 + 5n + 6 3 y = 506 n + 3 n + 2 = 506 = 23 22, n = 20 4 n n + 1 = 20 20 + 1 = 420 506 - = 86 86 4 + 420 3 = 1604 5 n n + 1 = n 2 + 5n + 6 - n n + 1 = 4n + 6 n 2 + n = 4n + 6 n 2-3n = 6 n n - 3 = 6 6 1 6 2 3 n 7 50 50 cm 2 600 50 = 12 350 50 = 7 12 7 = 84, 50 50 cm 2 84 视野情境扫描 2-3-9 10 2 10 1 10 10 1 1 2 3 3 5 4 7 10 2-3-9 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100 = 10 2 6 6 10 + 10 2 6 = 660 189
10 660 10 1 11 11 11 1 + 3 + 5 + + 19 + 21 = 100 + 21 = 121 = 11 2 11 + 11 2 6 = 11 12 6 = 792 12 12 12 1 + 3 + 5 + + 21 + 23 = 121 + 23 = 144 = 12 2 12 + 12 2 6 = 12 13 6 = 936 n n + n 2 6 = 6n n + 1 190
2 4 学习指导 知识点精析 1 1 2-4-1 1 2-4-1 2 2-4-1 3 2-4-1 2 2 1 191
360 2 3 3 2 4 1 2 2 1 2 1 2 4 180 6 360 4 解题方法指导 1 2005 7-2 180 7 7-2 360 180 7 360 360 2 2005 192
60 90 120 150 160 m n 60m + 160n = 360 m = 6-8 n 3 n m 3 2-4-2 1 2 3 4 2-4-3 2-4-2 2-4-3 360 1 360 2 n - 2 180 = n 10-2 180 10 = 144 360 144 144 193
3 2-4-4 2-4-4 4 2-4-5 2-4-5 4 2-4-6 12 0 5 12 2-4-6 1 6 2 6 n 6 12 6 12 6 12 6a 4 + 12 6a 3 = 6 0 5 + 12 6 0 5 = 39 m 194
基础达标演练 1 2 2-4-7 2-4-7 2-4-8 2-4-9 3 2-4-8 4 2-4-9 5 6 7 2-4-10 2-4-10 8 9 m n 1 n 2 n 3 n m m m n 1 n 2 n 3 n m 10 2-4-11 m 195
15 m 20 m 答案与提示 2-4-11 1 360 360 2 3 120 360 120 = 3 3 90 360-90 = 270 2 = 135 135 4 165 2-4-12 2-4-12 0 + 0 + 1 + 1 + 2 + + 1 + 2 + + 8 + 9 = 0 + 1 + 3 + 6 + + 45 = 165 5 60 + 90 + 120 = 270 6 120 135 m n 120m + 135n = 360 m = 3 - m 9 8 n n 196
7 2-4-13 8 2-4-14 2-4-13 2-4-14 n - 2 180 9 n n n 1-2 180, n 1 n 2 n 3 n m n 2-2 180 n 3-2 180 n m - 2 180 n 2 n 1-2 180 n 1 360 n 3 + n - 2 180 2 n 2 1 n 1 + 1 n 2 + 1 n 3 + + 1 n m = m - 2 m n m + n - 2 180 3 n 3 n 1 + + n m - 2 180 = n m 10 2-4-15 1 20 = 0 2 + 0 6 25 15 = 0 6 + 0 2 18 + 0 6 2-4-15 197
25 18 = 450, 450 0 6 + 0 2 m 0 2 + 0 6 m 25 0 2 + 0 6 m 0 6 m 1 1 1 1 450 450 + 25 = 475 450 2 + 25 = 925 2-4-15 2 视野情境扫描 1 180 2-4-16 2-4-16 360 2-4-17 2-4-17 n n 5 n n 5 2-4-18 1977 12 2-4-18 2 1 198
n 60 90 120 150 s t u v s + t + u + v = n { 60s + 90t + 120u + 150v = n - 2 180 s + t + u + v = n 1 { 2s + 3t + 4u + 5v = 6n - 12 2 v 3s + 2t + u = 12 - n 0 n 12 1 n 1 2 s t u v 2-4-19 2-4-19 199
热点题型分析 1 1 2004 2 2004 144 3 1 n - 2 180 n = 10 10-2 180 = 1440 2 36 360 36 = 10 7 7-3 3 = 14 2 2 1 2006 2-5-1 9 a 2 2005 2-5-2 1 2-5-2 2 MN MN 100 110 120 130 2-5-1 2-5-2 200
1 8 x 2x x + 3a 2x = x + 3a x = 3a 30a 2 M N, M = N = 90 = 60, MN = 360-60 - 90-90 = 120 1 30a 2 3 2004 108 60 90 120 144 108 2 + 144 = 360 热点考题训练 1 2004 36 2 2004 n 1080 n n = 3 2005 n n n 4 2005 2-5-3 2-5-3 201
5 2004 2-5-4 20 n 2 n 2-5-4 6 2004 1 2 3 4 5 7 2005 n 1 2 3 4 8 2005 9 2005 10 2004 2-5-5 1 2 1 2 1 2 l 1 2 1 2 1 2 1 3 l 3l 2l 2 3 l 2-5-5 2-5-6 202
11 2004 2-5-6 4 1 49 4 x y x > y 獉獉獉 x + y = 7 x - y = 2 4xy + 4 = 49 x 2 + y 2 = 25 12 2003 n 2n 270 n 7 6 5 4 13 2004 3 180 5 6 7 8 14 180 360 540 15 2005 2-5-7 F 1 1 1 1 1 F 1 1 1 = 2 2 2-5-7 203 2-5-8 16 2005 2-5-8 1 2 8 2-5-8 2 1 cm 2 17 2004 18 2-5-9 F = 3 = = = 8 19 2: 1 4: 3 20 1340 2-5-9
答案与提示 1 1440 36 360, 360 36 = 10, n - 2 180 = 10-2 180 = 1440 2 8 n - 2 180 = 1080 n = 8 3 3 4 n - 2 4 108 36 36, = 108 5 16 4n + 4 1 2 2 2 3 2 4 1 + 4 4 2 + 4 4 3 + 4 20 4 2 = 16 n 2 4n + 4 6 235 15 90 + 120 + 150 = 360 + 150 + 150 = 360 7 360 3, 3 8 9 108 360 108 10 1 2 = 1 3 2 1 = 1 3 1 2 = 1 3 2 1 = 1 3 1 2 = 1 3 2 1 = 1 3 1 2 + 2 1 + 1 2 + 2 1 + 1 2 + 2 1 = 2 3 l 11 x + y 2 = 49 x + y = 7 x - y = 2 x = 9 2 y = 5 2 4xy + 4 = 49 n - 2 180 2n - 2 12 + 180 = 270 n 2n 13 n - 2 180 = 3 360-180 n = 7 14 15 1 F 1 1 1 1 1 F 1, 1 + 1 F = 120 2 + 1 F = 1 1 F 1 = 120, 1 + 1 F = 2 + 1 F, 1 = 2 2 1 F 1 F 1 1 1 = 1 1 1 = 120, 1 = 204
F 1 = 60 = F 1 = 2, 1 F 1 3x = 5y 16 x cm y cm 2y - x = 1 5 cm 3 cm { { x = 5 y = 3 17 1 5-2 180 = 540 2 4-2 180 = 360 18 N F P F M 60 MF = MF = N = N = P = P = 60, MF N P, M= MF = F N = N = P = P = M = N = P = 60, MNP MN = NP = PM NP = N + + P = + + = 24 = 3 N = = 8, M = F = MF = MN - - N = 13 P = = 8, F = 3 F + + + + F + F = 3 + 8 + 8 + 8 + 3 + 13 = 43 19 2x x, 2x - 2 180 x - 2 180 4: 3 2x x 2x - 2 180, 3 = 2x 10 5 x - 2 180 x 4 x = 5 2x = 10 20 n 1340-180 < n - 2 180 < 1340 8 4 9 < n < 9 4 9 n, n = 9 1340 - n - 2 180 = 1340-9 - 2 180 = 80 100 120 3 30 1 90 2: 3: 4 1 2 3 3 140 205
4 4 10 5 27 6 m 7 n R R m - R n = 7 2-6-1 + + + + + F + G = 2-6-1 206 2-6-2 8 2-6-2 FGHI 6 cm 9 10 m n m + n = 360 m = n = 3 30 11 3 n n 12 13 100 14 n 1999 n 11 12 13 14 15 n 7 6 5 3 16 n n
n + 1 2n + 2 2n + 1 2n + 4 17 1 2 3 4 5 6 3 4 5 6 18 = = 78 142 140 130 150 19 2-6-3 1 = 2 3 = 4 5 = 6 7 = 8 + F = 120 240 300 180 20 n n - 1 2-6-3 2400 n 15 16 17 60 F FG 7 4 2 5 6 2 2-6-4 21 10 2-6-4 + + + + + F + G + H 22 10 FGH 23 10 600 24 15 2-6-5 2-6-5 1 207
2 3 25 15 1 2 2-6-6 1 2 1 2-6-6 2 3 2 1 4 4 2 n n n 3 74 答案与提示 2-6-6 1 60 90 120 360-90 = 270 2k 3k 4k 2k + 3k + 4k = 270 k = 30 60 90 120 2 8 α β α + β = 180 β = 1 3 α β = 45 360 45 = 8 n - 2 180 3 18 n n n = 18-360 n = 140 4 1080 180 180 6 = 1080 n n - 3 5 1260 = 27 n = 9 9-2 2 180 = 1260 6 125 m - 3 = 7 m = 10 n = 3 R = 5, m - R n = 10-5 3 = 125 7 540 2-6-7 1 + + F + = 360 + G + G + 2 + 3 + = 360 1 = 4 2 + 3 + 4 = 180, + + + + + F + G = 540 2-6-7 208
8 2 cm FGHI, = F = FG = GH = HI = I F = FG = FGH = GHI = HI = I = 120 I F GH, F = FG = G = 1 3 = 1 3 6 = 2 cm 9 60 + 90 2 + 120 = 360 90 + 120 + 150 = 360 10 90 135 1 2 m 90 + n 135 = 360 m = 1 n = 2 11 360 12 360 3 n - 2 180 13 n - 360 n = 100 n = 9 14 1980 < 1999 < 2160 180 13-2 < 1999 < 180 14-2, n =13 15 16 m m - 2 180 = 360 n m = 2n + 2 17 1 3 4 6 18 = 102 = 12 5-2 180 = 540, + + = 540-114 = 426 = =, = 142 19 + 4 + 5 = 180 F + 1 + 8 = 180, + F = 360-4 + 5 + 1 + 8 1 = 2 3 = 4 5 = 6 7 = 8, 4 + 5 + 1 + 8 = 1 2 360 = 180, + F = 180 20 α n - 2 180 - α = 2400 α = n - 2 180-2400 0 < α < 180, 0 < n - 2 180-2400 < 180 n - 2 { 180-2400 > 0 { n > 15 1 n - 2 180-2400 < 180 3 n < 16 1, 15 1 3 < n < 16 1 3 n 3, n = 16 209
21 G + H = HG + G + = +, + + + + + F + G + H = + HG + G + + + + F + G = FG + G + F + F = F- G = 360 22 F GH MNPQ 135 45, MNPQ P Q FMG NH GH = x H = y MQ = NP, MF + F + Q = N+ + P, 槡 2 + 6 + 5 2 槡 2 = 槡 2 2 y + 7 + 2 槡 2, y = 3 - 槡 2 MN = QP, x = 3 + 2 槡 2, 32 + 槡 2 23 n α n - 2 180 - α + 180 - α = 600, α = 90n - 390 0 < α < 180, 0 < 90n - 390 < 180, 4 1 3 < n < 6 1 3 n, n 5 6 24 1 108 360 2 2-6-8 2-6-8 3 2-6-9 2-6-9 210
25 1 2 3 4 56 4 26 2 1 2 + 0 8 2 2 + 1 8 3 2 + 2 8 n 2 + n - 1 8 n 2 + n - 1 8 = 8n - 6 3 8n - 6 = 74 n = 10 n 2n - 1 2n = 4n 2-2n n = 10 4n 2-2n = 400-20 = 380 74 380 211
1 2005 3-1-1 1 F 1 2 3-1-1 2 = 90 3-1-1 2 3 > > 3-1-1 3 3-1-1 1 读懂前面的材料再应用 是解这类题的关键 2 2 3-1-2 1 F 210
F 2, 3-1-2 3 3 3-1-2 2 FG HK HK S FG HK L 1 L 2 L 3 = a = b = c L 1 = 2S a + 2a L 2 = 2S b + 2b L 3 = 2S c + 2c ( ), L 1 - L 2 = 2S a + 2 a - ( ) 2S b + 2 b = 2 a - b ab - S ab ab > S a > b, L 1 - L 2 > 0 L 1 > L 2 L 2 > L 3, L 3 HK 大小比较通常用减法进行, 还可以用其他方法吗?试试看 2 2003 3-1-3 O F G H FGH, O = O O = O = 90 O = O 1 3-1-3, O O 2 OH OG Rt O Rt O 211
, OH = OG 3 OH = O = OF OH = O = OF = OG, G HF, FGH 4 1 2 2 3 3 4 3 4 O OG OG 1 2 3 2006 3-2-1 ' ' 90 90 90 3-2-1 ' ' = ' = + ' + ' + = 180 = 90 212
4 2005 3-2-2 = 4 cm = 10 cm F = cm, = 3-2-2 = x = 10 - x Rt 2 = 2 + 2 x 2 = 4 2 + 10 - x 2 x = 29 5 29 5 5 2005 3-3-1 O F 1 F 2 3-3-1 1 = F O = OF F F 2, = = F = F, - = - F, F = 213
, F 6 2005 3-3-2 1 = 5 = 40 = 45 3 F G F G H I IF J HF K 3-3-2 2 1 HIKJ 2 F H I K J F 3-3-2 1 HIKJ GFI FJ HGF KF 2 F 1 HIKJ G F, GF = F HI, GIF = JF GFI = FJ, GFI FJ, GI = J HG = K, HI = JK, HI = JK, HIKJ 2 F G F = 2 5 F 3-3-3 1 HIJK F, HG = K GI = J, HG: = GI: 214
>, GI > HG, K > J, F K J 3-3-3 3-3-3 2 F J K H I F = x HG = = 45 = 5, = 5 = GI G = HG = 5-2x = 40 3-5 GI, G: = GI:, 5-2x : 5 = 5: 40 ( - 5 3 ), x = 1, F = 5 - x = 4 F, 5 2 F 4 7 2005 3-4-1 1 G G G GF G H 1 1 G 2H 215
2 G H 3-4-1 1 G = G 1 2 H = G 1 1 GF, = G = G = = 90, G 2 G, G = G = GH, 180 - G - G = 180 - GH -, HG = G = 90 H 2 H = = = 1, = 槡 2, = - = 槡 2-1, G = = 槡 2-1 G = 槡 2-1 H 8 2005 3-4-2 1 Rt PMN P = 90 PM = PN MN = 8 cm 8 cm 2 cm M MN Rt PMN MN 1 cm 3-4-2 2 N x PMN y cm 2 y x 216
3-4-2 PMN Rt PMN Rt PMN PM = PN P = 90, PMN = PNM = 45 PM PN G H G GF MN F H HT MN T = 2 cm, MF = GF = 2 cm TN = HT = 2 cm MN = 8 cm, MT = 6 cm 1 cm Rt PMN 1 M F 0 x 2 3-4-3 1 PM Rt M = = x, y = 1 2 M = 1 2 x2 0 x 2 3-4-3 2 F T 2 < x 6 3-4-3 2 MG M = x MF = 2, F = G = x - 2 = 2 217
, y = 1 M + G = 2x - 2 2 < x 6 2 3 T N 6 < x 8 3-4-4 3 PN Q MQHG M = x, N = Q = 8 - x 3-4-4 = 2, y = 1 MN + GH 2-1 2 N Q = - 1 x - 8 2 + 12 6 < x 8 2 9 2005 F F F P 3-5-1 1 1 3-5-1 2 2 3-5-1 3 3 3-5-1 4 4 3-5-1 5 218
3-5-1 1 = 90 F 3-5-2 1 = 3-5-2 2 3-5-2 2 = 2 = 90 = 30 F 3-5-2 3 3 = 90 = 2 F 3-5-3 1 = = 90 3-5-3 2 3-5-3 4 > G = G F G F F 3-5-4 1 219
> G H H HF = G F 3-5-4 2 > G = G F G F F 3-5-4 3 3-5-4 10 2005 a FGH 3-5-5 G 3-5-5 N 1 N 2S + S FGH = S N 1 a b a > b FGH 3-5-6 3-5-5 M M M MN M N MN N N 1 MN a b MN 2 3-5-6 FGH MN 3-5-5 2 n n 2 3-5-6 220
1 MN M Rt 2 = 2 + 2 MN a b N NP 6 2 1 1 1 MN Rt M Rt = M + M = + M = 90, M =, Rt M Rt, M =, MN a 2 + b 2 2 = 2 + 2 = a 2 + b 2, 3-5-7 MN 2 N NP P 3-5-7 6 5 4 3 2 1 6 5 4 3 2 1 MN 2 n n - 1 11 2005 = 8 = 6 1 3-6-1 1 3-6-1 2 3-6-1 3 S 1 S 3 S 1 = S 2 = S 3 = S 2 221
3-6-1 3-6-2 2 3-6-2 O 3 1 S = S + S = 1 2 O + 1 2 O 3-6-1 1 S = 1 2 6 3 + 1 2 6 5 = 24 3-6-1 2 3-6-1 3 24 2 1 24 3 24 1 24 24 2 O 24, S = 1 2 O S = 1 2 O = 24, S = 1 2 O + 1 2 O = 1 2 O + O = 1 2 3 24 12 2005 3-6-3 = m 222
m n m m 3-6-3 3-6-4 1 3-6-4 2 12 3-6-4 3 3-6-4 1 3-6-4 4 2 m 3 3-6-4 5 m 4 3-6-4 6 n n m 223
2 3 4 1 3-6-5 2 m m 3-6-5 m m 3 m m 4 m n m 224
13 2005 3-7- 1 i 1 F = 7 75 F F i 2 i 2 < i 1 M = h F S 2 1 i 2 = 1: 1 7 h = 3 M 2 i 1 i 2 h S i 1 i 2 h h l 3-7-1 i i = h l 1: m 1 M F FN N MN = F N N FN N = 1 1 7 2 i 1 i 2 1 F FN N 3-7-2 MN = F = 7 75 m FN = M = 3 m i 2 = FN N, N = 5 1 m, M = MN + N = 7 75 + 5 1 = 12 85 m 2 i 1 = M M, M = h i 1 N = h i 2 = M - M = MN + N - M =7 75 + h i 2 -, S = 1 F + M 2 = 1 7 75 + 7 75 + h h 2 ( - i 2 i ) h S = 1 2 ( ) 15 5 + h i 2 + h i 1 1 h h i 1 3-7-2 225
14 2005 獉獉 360 獉獉 x y 60 x + 120 y = 360 x +2y =6 x y x = 2 y = 2 x = 4 y = 1 2 2 4 1 3-7-3 1 2 3 1 x y 3-7-3 4 獉 獉獉獉獉 2 3-7-3 5 3-7-3 1 3-7-3 x y 2 180 6 1 x y 60 x + 90 y = 360 226
2x + 3y = 12, x = 6-3 2 y x y, y = 2 x = 3 3-7-4 1 3-7-4 2 2 3-7-4 3 3-7-4 综合训练题 1 2005 3-8-1 F F 8 F 22 F 2 2004 3-8-2 a b c d 3-8-1 3-8-2 b 3-8-2 227
1 b a b c d V 7 9 F 3 2 3 20 11 2 3 2004 3-8-3 M N MN P Q PQ = 3-8-3 3-8-4 4 2004 3-8-4 n 1 2 3 4 5 n 4 7 10 5 2006 3-8-5 F = 50 F = F 3-8-5 3-8-6 228