ONTNTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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- 汝 滑
- 7 years ago
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1 !!!!!!!!!!!!!!!!!!!!!!! 1!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!! !!!!!!!!!! !!!!!!!!!! !!!!!!!!!!!!! 1 2 1!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! 1 6!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!! !!!!!!!!!!!!! !!!!!!!!!!!!! 2 4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!! 210!!!!!!!!!!!!!!!!! 210
2 ONTNTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
3 学习指导 知识点精析
4 S = = F 问题探究 = = 180 = = = = 3 = = = F
5 解题方法指导 = 110 F F 1 + F = F 1 + F F F = = = , = = 110 F =, F = F + F = 180, + F = F F = 135 = F = F + F = 360, = 45, = = 45, + = 180, = 135 =, = F
6 cm O O O 7 cm O O = O O = O O O 50 cm, = = O= O = 50, + = 25 1 O+ O + - O + O + = 7, - = = 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 F F F = 60 = 2 cm F = 3 cm F F = 60 F = 120 4
7 = = 60 = F = 30 F 30 F F F, = F = 90 F F = 60, = F - F = ,, + = = 180, = = 60, = F = 30, = 2 = 2 2 = 4 cm = 2F = 2 3 = 6 cm, = 槡 2-2 = 槡 = 槡 12 = 2 槡 3 cm F = 槡 2 - F 2 = 槡 - 3 = 3 槡 3 cm, = 2 + = = 20 cm, S = = 6 2 槡 3 = 12 槡 3 cm 2 S = F = 4 3 槡 3 = 12 槡 3 cm F = F = F F
8 6 F F F F F, =, = F F { = = F = F, F SS F, = F O F F O F 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
9 , = F =, - = F - = F 1 2 O = OF = F 基础达标演练 1 = 35 = = 2 20 cm 18 cm MN M M = 6 M N NM 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 = = = = O O O O
10 = S = 6 cm 2 5 cm 2 4 cm 2 3 cm F F F = F F = F = F F F G H 1 2 F F G H F F F 1 = F 2 F = F F
11 F 1 F 2 F F 答案与提示 = + = cm = N = M 9 N= M = M = M cm 4 cm - = 3 cm + = 11 cm = 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 =
12 = F = 2, = + F = F, F = F 14,, = = 1 S = S F, F, F F, F = F 2, F, = = F = + + F 难点指津 ,, 2 = 3 3, 1 = 2, 1 = 3, = = 3, 1 = = = ,, 2 = 3, 1 = 2, 1 = 3, = = = 3 = = = 20 = = 4 = = =
13 综合延伸 Q N N Q N Q N P Q N M P M Q Q N Q Q P M Q Q,, + = 180 Q Q, Q = 1 2 Q= 1 2, Q + Q= = 90 2, Q = 90, Q Q 11
14 km 125 km 100 km 14 L km = 375 = + 125, = = 500, = =, 2 + = = 1750, = 245 L , = 931, = < 2600, = km 14 L 1 km 14 L
15 a b P Q a M N b PM QN a b PMNQ PM = QN a b P Q a a a M N b b a b a b M P N Q a b P M 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
16 思维拓展测试 F F F M 1 N F 2 M 2 N 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 N 1 N 2 2 F F F FG P MP F F F G 1 G H 2 G N H G F G PH P H H PG H PG 14
17 G F G PH P H P M GH N MN = 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 S cm 2 t S 答案与提示 1 = F F = = F F n n n = 4 1 M 1 M 1 n = M 1 M 2 M n n n n n n n = 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
18 S G + S FG S G + S HG, 5 1 P 2 P = 2 cm = 60 = 1 P = 槡 3, S P = 槡 t 6 P Q PM QN F Q = t F = 1 2 t QF = 槡 3 2 t P = t + 2 = t P = 槡 3 + 槡 3 2 t, S = 槡 3 2 t + 槡 t 8 P Q PM QN F Q = t F = 1 2 t F = 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 t 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 槡 3 t S 槡 3 2 t + 槡 t 6 S = 5 - 槡 3 8 t 槡 3t - 34 槡 3 6 t 8 3 槡 3-30 槡 3t 槡 3 8 t 10 2 t2 2 t2 16
19 视野情境扫描 O O' O' O 2 O 17
20 1 1 2 学习指导 知识点精析
21 问题探究 O O = = 2 O = O O = O 5 19
22 解题方法指导 M N P Q M = N = P = Q M MNPQ Q P N 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
23 F F = F = F F F = F = F, F = F { F = F = F =, F SS, = F =, =, = 2 = 30 3 = 4 = 38 F F
24 = = 1 = 2 = 30 3 = 4 = 38, = = 68, = = = 112 = = = 112, = F, F = 3 = 38 F = 4 = 38, 2 + F = = = F = = = 68, =, F = F F F O = F O O = OF O, O= O O = O 22
25 = F O + O = OF + O, O = OF O= O, F M N M = N M NF F MN F 1 M 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
26 , MFN, MN F = F M N F FM = N M F N 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
27 F F = 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 O F O O O = OF O = F F O F F 25
28 26 7 = = = = = = = 8 = = = 9 F F F F = F F = 3 5 F = = 1 2 = G H G = H F = HFG G F H F = = F = F = F F F = F = F = F F
29 F F 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 O F 6 = F 7 8 = , = 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
30 , 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 = 60 F = 2 F = 槡 3F
31 = 90 = F = F = 1 2 = 1 2, F =, F =, F, F = = 2 = 2, = = 60, = =, 1 = = 30, = 90 Rt 2 = 2 + 2, 2 = 2-2 = = 3 2, = 槡 3 = 槡 3F 9 O 5 1 2O= O 3 = 4 =
32 5 1 2 O O O= O O = O = ⅰ 1 2 ⅱ 1 3 ⅲ 1 4 ⅳ 2 5 ⅴ ⅰ ⅱ O ⅲ O ⅳ 思维拓展测试 = 3 = 4 =
33 O F F F = F = F = F = F O F F > F 1 F 2 F 3 > < 答案与提示 F 4 F Rt =, = 45, =, = = 45, F = = 45, F + = + = 180, F F = = 90, F F = =, F = F M M F 31
34 M = F MF 2 F + = F = - F + = 1 F = M = - M = - 3 F + = F + = 视野情境扫描 v 1 m/s v 2 m/s M F 1 F 2 F 1 F 2 F F 1 F v 1 F 1 F v 2 2km h 4km h M F km/h 4 km/h 32
35 学习指导 知识点精析 1 獉獉獉獉獉
36 = 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 = F = GH
37 解题方法指导 O O = 120 = 6 cm O 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 O F F F = F O
38 = 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 F G H FGH + = = = 1 2, = 1 + = H G F 2, = 90 36
39 G = 90 H = 90, GH = H = 90, FGH MN Rt MN MN = M F F = F N 37 F 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
40 = F = F, F F, F = F F G H = 2 = H F G O F O F F 1 H F GF GH S H = S F = S GF = S GH = 1 2 = = 1 H = 1 = 2 2 S H = = = 1 S - 4 S H = 2 O FO 1 O O
41 O = 8 cm O O = 8 cm O = O O= O O = O O, O = O, O= O = O = O =, = 8, O= O = O = O = = 4 = 90 2 = = = 48, = 4 槡 3 = 4 4 槡 3 = 16 槡 3 cm 2 60 基础达标演练 O O = 2 O = 18 cm = cm k 2 k = 39
42 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: F F : = 3: 2 O O = = =
43 O = O O = O = = = 90 + = 180 = = = M 1 M M 2 M = M M = 2 = O = O O O = O O = = = 90 M N MN = F F G F H HFG N M G F H
44 答案与提示 1 9 O = 2 O = 60 = 90 = 30 = x y n ny = 2x x = 2y n = 4 k = O= O 5 7 Rt = 4 = 3 = = 7 = 7 6 1: 2 = 槡 3 8 x y z z = x y 1 z2 = x 2 + y x = 3 4 y x y = F, = F = F, S = S F = S F = 1 3 S S = 1 2 S, S F = = 90 : = 3: 2, = 54 = 36, = 54, = = 36, = - = , = = = 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, = = = 75, = 90 - = = 15 15,, 42
45 , = =, = 16 = O O = 75, O = 30, = 90, O = 60 O = O, O, O = 60 = O, =, = 45, = = 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 M N = 2 MPNQ, = M N M, M P Q = N N, MN = N = N, N = N MN = N , P M MPN = 90 MQN = 90, PMQN MPN = MQN =90 PMQN PMQN 43
46 综合延伸 F O F F G O OG = 30 OG = 1 3 G 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 = , = G = G = OG OG = 1 3 =
47 F = 3 cm = 8 cm cm 2 F F = 3 = = 8 = F = 5 F F, = = 8 = = 3 = 5 F, = F = F = 5 Rt F F = 槡 F 2-2 = 槡 = 4 F = x = F = x + 4 Rt F 2 + F 2 = F x 2 = x x = 6 F = 6 = S F + S F = = 30 45
48 O O MN M F 3 O 1 O = OF O F 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, = = 1 2 = = 90, F 思维拓展测试
49 FGH H = 3 F H = 5 M = 6 cm = 9 cm N G 1 F F F F F G G cm G 1 F 2 F M M = M O P M F = F F F F = cm 30 cm 80 cm 45cm
50 80 cm P H Q F 45 cm = 3 槡 3 = 6 F P Q PQ H P = 30 1 QF 2 PFH > O O M N 1 S MN = S NM 2 MN MN M: M N O P M P P S P = S P + S P P F F S P + S P = 1 2 PF 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
51 P S P S P S P 49
52 P 1 P 2 答案与提示 FGH = F = 3 = F = 3 G FG G = = 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 = x Rt P P = 30, P = 2x P = 槡 3x = P = 2x + =, 3x = 6 x = 2 = 2 50
53 , = 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 = = S F = 槡 槡 3 S HFQ = 1 2, S PFH = S PFQ - S HFQ = S F - S HFQ 15 = 槡 3 - 槡 3 = 槡 3 1 槡 3 = 槡 ON OM N = M N = M 2 MN 3 S 1 = 1 2 N = 1 2 M S 2 = M = M S 2 = 1 2 S 1 M = M M: M = 1: S P = S P + S P S P = S P - S P P F F S P = 1 2 PF = 1 2 P F P F = 1 2 P F = S P S S P + S P = S P + S = S P S, S P = S P + S P 51
54 视野情境扫描 槡 M M N N M M N N
55 1 2 2 学习指导 2 5% ~ 8% 知识点精析 1 獉獉獉獉獉
56 4 a b S = 1 2 ab S = 1 ab 2 问题探究 O O F O F F = F F F F = = = F O= O O = O F = OF = O F F F 解题方法指导 54
57 cm = = 15 cm 1 1 = = = =15 cm =60 =60 1 = cm 1: , 6 + = 180 = 2, = = 60,, = = 6 cm 6 cm 1: 2 1: F H F G 1 H G F F
58 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 O 1 = 2 3O= O 4O = O
59 Rt = 90 = 60 F F = F 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
60 , F = F, = = F = F, F F O F O F F = 2 cm = 4 cm F O F F, O= O, FO = O OF = O, OF O, O = OF, F F, F, = = x = x = 4 - x Rt 2 = x 2 = x 2 x = 2 5 = 2 5, S F = = = 5 F 5 cm 2 基础达标演练 58
61 = 65 = = 3 40 cm 12 cm = 60 = 4 cm = = F F F = F = = 80 F F F cm 5: cm 2 1 cm 1 05 cm cm 10 = 120 : F 槡 3: 3 槡 3: 2 槡 3: 1 1: = 4 cm
62 F H = F = 60 = 20 F F = F 1 F 2 G F H G = 25 = 130 H F F G F F O O F F F = 400 m F = 300 m 60
63 答案与提示 1 50 = = = cm cm 4 槡 3 cm = = 7 8 F = 40 = 100 F F = 40 F = 60 = F : = 120, = 60, = = O O= 槡 3 2 = 槡 3, : = 槡 3: , =, =,,, = 60 2 = 120 2,, O = 1 2 = 1 2 = = 2, O= 槡 2 - O 2 = 槡 S = 1 2 = 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 = + = = 80, F = - F = = 20
64 13 1, = = = = = F, F 2, = = 130 F, = F = 25, F = 80 G, H + F = 180, H = , 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 = = 76800m 2 槡 2-2 = 70, = + = 320 难点指津
65 综合延伸 M N M =2 N M P P Q N M Q PMQN N 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
66 = F MF 1 F M 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 =
67 =72 = 72 = = 108 = = 180 思维拓展测试 1 O 1 = = 4 5O = O F 2 5 P P P P PF F F F F = = = a 60 a 1 2 a 槡 3 2 a 槡 3a
68 FG G F F F = F 1 F 2 F O O F F 1 O OF O 2 F F F 66
69 答案与提示 S FP = S P, S = 1 2 S 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
70 学习指导
71 知识点精析 问题探究
72 3 4 解题方法指导 = F F F F = + = = 2, = 45, =45 =, =, = 1 = F = + F, F = =
73 F O G G O F G 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 F F = 45 F = + F 2 1 F G
74 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 O = = O = O = O = O = O = O O = O = O = O = O = O 72
75 FGH G P F 5 6 N 2 Q H M FGH FGH FGH, H F, 1 = 2 = 45 = = 90 F = G = 90, FGH = 3 = 4 = = 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
76 16 cm = F F F F ' ' ' ' = 槡 2 ' FG H H F F = F F G = F G F F + = 90 F + G = 90 H F G G R P F Q = P PQ Q PR R PQ + PR 1 2 槡 2 2 槡 = 1
77 槡 2 2 槡 2 2 槡 O = = = O = O = O = O F F = = = MN M = 35 NM = = 75 N F M cm F F F = F F = F = F F H G F G K F G = G + F FG G H H = K K = KFH F
78 答案与提示 槡 2 1 O = 45 = 3 20 = 2 = 4 F = 4 S F = = 4 H F GF HG S FGH = S - 4 S F = = O = 22 5 O = O = 45 = = 67 5 = = 4 5 = 90 F = = 90 F 6 槡 2-1 = 槡 槡 2 2 ' = 1 ' = 槡 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 PQ PR + PQ = O F F F = F = = 1 = 槡 2, = 槡 F MN F NM = F = F Rt F Rt F = M = 35 = =, = = 75, = 30 = 90 =, = = = 120, = 30 15, = 90, = 槡 2 + = 2 槡 5 S = 1 F = 8 2, F = 8 5 槡 5 cm 2
79 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
80 综合延伸 P P PF F P F 1 P = F 2 P F P H 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
81 , = 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 F F = F O H O F F F F = O = 1 2 F FH = O F FH H 79
82 O O = 1 2 = 1 2 FH, FH = O = 1 2 = 1 2 F, Rt FH FH = F, 2 = 3 = 15, = 45, 1 = 15, 1 = 2 = 3 = 15 F P Q F F P O 1 PQF 2 P Q 3 PQF 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
83 , FP = PQ = Q = F PF = PQ FPQ = 90, PQF 2 P O P =, P O, P 3 P PQF P PQF H H Ⅰ Ⅰ M F F 200 G G N F Ⅱ Ⅱ FG M HG N S NH + S FM + S NMG = = a a 2 = a = 100 槡 5 NH FM 100 槡 5 H F H F H F H F 81
84 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 = 槡 = 100 槡 5 F = 槡 = 100 槡 5, H = F = = HF, FH F = 90, FH FH 思维拓展测试 l S 1 S 2 S 3 S 4 S 1 + S 2 + S 3 + S 4 = S 1 S 2 S 3 S 4 l cm 4 槡 3 3 cm 2 82
85 H S S S 1 S 2 S 1 S 2 S 1 > S 2 S 1 = S 2 S 1 < S 2 S 1 S O F F H H H = 1 F 2 H F F O G H F G H G F H
86 方法一 方法二 方法三 GF G F G F P M H F M P P M PF M F 1 PMF 2 1 P PMF a 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 = 槡 3 H = 2 3 槡 3 H = 4 3 槡 3 H = 30, ' = 30 G 84
87 3 S 1 S 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 方法一 方法二 方法三 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 , 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
88 , 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 = 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 O O O O O F O
89 1 3 学习指导 4 ~ 知识点精析 上底 腰高腰 2 3 下底
90 S = O 1S = S 2S O = S O 3S = S 问题探究
91 解题方法指导
92 = 70 = 40 = 6 cm = 15 cm = 9 = 1 = = = 70, 1 = 70 = 40, 2 = = 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 cm = 5 cm F F F = = = F F F = 90 F F 90
93 = 1 2 F F F, F, F = F =, =, = F F, F, F F, F, = 1 F 2, = F = = = 4 2, S = = cm = = =
94 = = = = =,, =, =, =, =, =,, =, 基础达标演练 1 = 55 = 78 = = cm 13 cm 3 = 60 = = 4 cm = = S = cm 60 4 cm 6 a = 16 cm b = 13 cm c = 10 cm d 7 2: 3: 3:
95 = = 30 = 60 = 2 4 槡 3 3 槡 = = 8 = 10 = 6 16 槡 槡 5 32 槡 槡 = = = = 90 = 45 F F M F F = = F M = F = 2 F = 2F = F = 93
96 2 = 2 = 60 F = 90 = 2 F F F F 答案与提示 = = cm 3 2 cm 2 槡 3 cm 6 槡 3 cm 2 = 2 cm = = 2 槡 3 cm = S = = 6 槡 3 cm = = cm 8 cm cm < d < 13 cm 10 cm = 3 cm = 60 = = 90 = = 90 = = 2 = = 2 = 4, = 6 11 F F = F = F = 6 Rt = 8 = 2 = 2 槡 15 S = 槡 15 = 16 槡 15
97 12 =, = = 120, = = 30, = = 30 =, = = 75, = 60 = 75 = 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, G G = = 90 G = 90, G, = G = 2, G = G, =, = F F, F 难点指津
98 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 O 综合延伸 3 F =2 1 2 = 60 = 2 S F
99 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 = 槡 3 = 3 槡 3 97
100 mm 500 mm 300 mm 600 mm 250 mm mm = mm
101 = 90 = 14 cm = 18 cm = 21 cm P 1 cm Q 2 cm P Q Q F t t 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 Q QFP = Q = - Q = 21-2t, P = P - = t t = 3t - 21 PQ, QF = 1 2 Q - P = 1 2 PQF, P = QF, 3t - 21 = 3 2 t - 9 t = 8 P 2t t = 3 t t = 8 PQ 思维拓展测试 = 60 = = 2 = 6 =
102 M N = = = 1 = 60 MN P MN P + P 4 = > = 13 槡 2 + = = = = + = 180 = = = F F F 1 F = 2 F = 5 = = a = b h c c = a b h
103 3 = 3 = 7 = 5 槡 : 1 2 M F N 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, = = = 180 = + = 180 = = 90 = =
104 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 = G 2 = 100 G 2 = 100, 2 + G 2 = G 2, G = 90 G G, 8 1 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 M = M N = N, MN, MN, MN F MNF, M N N, MN = 视野情境扫描 102
105 J Fields 学习指导
106 知识点精析 = 5 问题探究 P P
107 解题方法指导 cm FGH cm FGH cm 2 H G F F F S F = F G H F F = 1 2 HG = 1 2 H = 1 2 FG = 1 2 F = FG = HG = H = 1 2 = = 4 105
108 = 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 = = 槡 > 1 2 = 1-2 F F F 1 F, = F = 90 = F =, F, = F F = =, F 2 = F =, = 1 F 2, = F =
109 = M P N MN Q P Q P M N Q 21 G 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 F F 107
110 F = 6 + = 12 = = = = cm =, =, =, =, = = = 1 2, = = = 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
111 4 Rt = 90 F = 4 cm = 6 cm F F F = 2 = = 5 cm = 12 cm cm F = 120 = 2a F O FO - O = = cm 9 2 cm 9 cm 12 cm 18 cm F O F G = F G = 20 = 66 FG
112 = 40 = 50 M F N F = a MN = b a + b a + 2b 2a + b 2a - b O = F OF = 1 2 F N M F O Q P M N M N P Q MNPQ G G G G F G P M P F = 1 P F GH = G = G = 18 = 32 F + GH M F G P G F H H G F = F F H G H G 答案与提示 1 40 cm 2
113 3 16 cm 24 cm 2k 3k 1 2k + 3k = 20 2 k = 8 2k = 16 3k = cm 3 cm F = 90 F F = 1 = 3 cm 2 = 1 = 2 cm F F = =, = = = = 90 = = 5 = 12 = 13 = + = = = cm a = 30 = 90 = 1 = a 2 1 = = a 2 a + 2a = 3 2 a 8 9 F F O, O = 1 2 OF = = OF - O - = = 1 = = FG G FG 1 = 2 G = = FG = G = 20 = 66 GF = 134 G = GF FG = = N NH NG H G GNH = 90 MN Rt GNH MN = 1 2 GH = 1 - = b, - = 2 2b F, + = 2a = a + b 13, = =, F =
114 F F = F, F F, F = F O = O, OF = 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 = M FM M F = F M = M, FM = = M = M, M = =, FM = M MF = MF M, MF = G FM,, H = G 难点指津 MF = H O F F = 1-2 F G G, G = 1 2 FG, FG = H O F G
115 , F = G - FG = 1-2 F G G F G F H G G G F G F G 综合延伸 = O O = 60 F G F O O O FG O G F = 1 2 = G FG O = 60 O = O O O O = 90 G G = 1 2 FG = 1 2, = =, =, O 113
116 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 = a = 1 2 = 1 2 a ( ) 2 2 = = a + a = 3 4 a = = ( 4 a + a ) = 7 8 a n n n - 1 n - 1 n n n 1 n n n n = = 1 2 a = 21-1 a 2 1 n = = 3 4 a = 22-1 a 2 2 n = = 7 8 a = 23-1 a 2 3 n n = 2n n a 114 1
117 1 2 3 思维拓展测试 ' ' F =3 cm F =4 cm ' + ' = cm 20 cm 2 S GF F G =2 槡 2 cm 2 cm F G F cm a n n n n n n n n 5 F 2F + 2F = + 2F > + 2F < R P F P RP P R F F F F = F G O OF = 2OF
118 R F P F G H G HF = = 6 = n n n n n n n n 答案与提示
119 4 = F F = =5 cm ' + ' = - '' = - =5-3 =2 cm = =500 cm 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 2 a2 S = 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 = 1 = = x 2 2 =2x x +10 =4x x = = = = =50
120 , 1 1, = = 1 2, = 1 1, , , 1 =90, S = = 24, S = = 12, n n n n 2 24 n 视野情境扫描
121 1 5 学习指导 知识点精析 问题探究 119
122 120 解题方法指导
123 = = = > F P F F F F, F F, F, F F F F P, P F, F, F
124 基础达标演练 1 F F F F h F h F a + b > 0 a > 0 b > 0 a > - b > 0 b > - a > 0 a > b > 0 b > a > 0 a b P 1 P P P 答案与提示 122
125 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 4, > = 1 1 > 1 4 难点指津 综合延伸 123
126 124
127 4 n 5 O F 6 O O< O < O O O > O > 60 O > 60 O > 60 OF > 60 FO> 60, O + O + O + O + OF + FO> 360 O + O + O + O + OF + FO= 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
128 126 m x x 思维拓展测试 P P < P 答案与提示 1 2, 3 P 1 P P > P < P 2 P P P > >, P > P <, P 1 2 P P
129 = = = = = RQP RQP 2 R P S S = 1 2 S QP S S = 1 2 S R S = S + S 1 2 S QP S R = 1 2 S RQP < 2 1 = 1 2 S = 视野情境扫描 L Lemhus = = 127
130 ' ' ' ' ' ' ' ' = ' ' = ' ' 1 = 2 < > < < = 1 2 < 1 = 2 ' ' ' = = + > + = = ' ' ' ' ' ' > ' ' ' 1 = 2 3 > 4 ' ' > ' ' > = = < < 1 2 < 1 2 < > < < > =
131 1 6 学习指导 知识点精析 O O 解题方法指导 1 O
132 O 2 O 基础达标演练 O
133 答案与提示 O O
134 视野情境扫描 O
135 热点题型分析 = 1 P P P = = F = F = F F F F, =, = F F 133
136 { = = F = F, F, = F = F 1 F 2 = 12 cm F 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 = 90 F F = 1 2 F
137 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 = 50 =
138 = = 8 cm = 6 cm cm = 60 P P = P = 2 槡 3 P = 3 = 2 F F = 2F F M M M 48 cm cm ' 1 64 cm 7 cm O M 136
139 M = 2 N N + MN FG F S S = 2 S = 2 4 S = 4 S F G = 2 O F O O O O O O O O FO
140 O O = 6 cm O 6 cm 4 cm 3 cm 2 cm F G H S 1 S 2 S 1 > S 2 S 1 < S 2 S 1 = S 2 F F O O 1 O = 槡 3 = 1 1 ( ) 3 ( ) 槡 槡 3 2 ( ) 1 ( ) 槡 槡 F = F F O O
141 F O O F F O = OF = 90 F F = F F F = 1 2 G F H GH cm F 1 = F = 60 = F = F F P PF FG Rt = 2 = 60 Rt FG F ' ' ' ' ' '
142 1 ' ' ' 2 ' ' ' F 0 1 G G F F 答案与提示 = = = = 90, = 槡 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 = 10 槡 槡 3 = 20 槡 F F = = 8 cm = 90 = 10 cm S = 1 2 = 1 2 F F = cm
143 7 2 槡 3 4 槡 3 P, = = 60, = = P = P, P P = 2 槡 3 P P = 4 槡 F = 2 = 1 F = - - F = = M M M = M M = 90, M = M = 45, M =, = 2 + = 24, = 8 = 16, S = 16 8 = ' + 2 = 64 2, 2 = = = , 7 64, 槡 = 槡 2 2 = 1 槡 M N N + MN M M F F S F = S = O FGH S = 141
144 1 2 G FH S = G FH O = 槡 3 = 1 O = 2 O = 90, O = 30, 1 O = 30 1 O = y 1 = 1 2 O 1 = 1 2 O = 槡 3 2 O = ( ) 槡 , = = = 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 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 = 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 =
145 ' ' ' 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 ' = 槡 : 9 78 cm cm cm cm : cm = 4 cm : = 2: 1 = = 5 = 8 F F = P = 4 M M P PF
146 O F = 12 O: OF = 1: 2 = 9 10 > = 2 = a = b = 1 2 O = 4 cm O 12 4 cm 3 cm 2 槡 3 cm 4 槡 3 cm = 30 = 槡 2 槡 6 槡 S 槡 S 1 2 槡 S 1 2 槡 3S 1 2 槡 5S 16
147 = = O O G O O = OG G G = G G G = G F F 64 F = 30 = 60 = 槡 3 4 槡 F G F H HFG = 20 cm F 145
148 F = 40 m F = 30 m F Rt = F O F = 2 1 = 槡 2 2 = 2 槡 2-1 F F F F 1 1 F 2 2 F 答案与提示 x cm 9x cm 4x cm 9x cm 4x + 9x + 4x + 9x = 78 x = 3 12 cm 27 cm cm 2 6 cm 4 12 cm , cm, 4 3 = 12 cm 槡 3 cm, = 90 : = 2: 1, = 30 = 90, = = 2 = 4, = 8 3 槡 3 = 8 3 槡 = = 5 = = 8 146, = =, =, = = F, F = + F - = + - = = 2
149 7 4 S P = S PF, S M = 1 4 S = = O: OF = 1: 2 F = 12, OF = 8, = 2OF = a + b , = = b = = a = = 2 = + = 2,, = + = + = a + b =, = = a 11, = 180 = 1, = 60 2, = 90 - = 30, = 2 = 8 cm = = 4 槡 3 cm O= O, O = 1 2 = 2 槡 3 cm 槡 = + = 180, + = 180, 13 Rt = 30 = 2, = 1 2 = 1 = 2 2 槡 - = 槡 3 2 = 槡 , = 2 = 2, Rt = 槡 = 槡 槡 2 = 槡 7 14 ( ) 15 2x x 2 x + 2 S = 1 2 x 2x = x2 = S x = 槡 S, 槡 槡 S = 槡 S 2 槡 2 = 槡 5 2 x
150 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 = = 50 = 10 = 8, Rt = 槡 2-2 = 6 S = = = 2 槡 3 = 6 F Rt F Rt F F = 1 = 1 F = + F = 3 = 2F = F G HF G FH G = HF 22, =, =, =, = =, =, + = 90, 3 = 90, = 30, = 1 2 = = = x = 2x, 5x = 20 x = 4, = 4 = 8 1, = 6 cm 2 23 F,, OF = O F, O = O OF = O = 90, OF O, OF =, F F, F, S F = 1 2 F = = = 2, = 2 F, = = = x = - = 2 - x Rt = 2
151 2 - x 2 + 槡 2 2 = x 2 x = 3 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 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
152 2 1 学习指导 知识点精析 1 2 k k
153 问题探究 k
154 解题方法指导 = = = 认真观察瓷砖铺设的图案, 为后面的图案设计作好准备
155 cm 2 x cm y cm x + y = 60 { 2x = x + 3y x = 45 { y = cm 15 cm
156 = < 360 <
157 基础达标演练 X X
158 答案与提示 = = = α 3α = 360, α = = 60,
159 难点指津 1 155
160 2 综合延伸 cm 20 cm F G H 4 2 m 2 8 m = m 2 8 m 30 cm 20 cm = m = 0 06 m 2, = , 4 2 m 2 8 m 30 cm 20 cm =
161 =
162 思维拓展测试 n n n n
163 5 I cm cm 1 cm
164 答案与提示 1 1: n n n 8 + n = 5n n - 6 n n 8n 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 = x 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 = 视野情境扫描
165 学习指导 1 2 知识点精析
166 1 2 n n n 3 n n n - 3 n n n n n
167 3 1 n n n 360 问题探究 n - 1 n n n n n P n n - 1 n - 1 n P n n = n O n n n n 180 O n n = n n 180 n
168 n n = n n = 360 解题方法指导 = = n n = 540 n = n n n 2 9: 2 n n n n : 360 = 9: 2 n - : 2 = 9: 2 n =
169 m n m n = 1800 m n m n m n = 1800 m + n = 14 m n 2 14 m = 10, { n = 4 { m = 8 n = 6 { m = 6 n = 8 m = 4 { n = = 2 = 135 = 100 = NM MN MN 1 = 2 1 = 2 1 = MN 165
170 , 2 = MN,, MN + MN = 180 NM = 540, = MN - MN = = = = = +, 1 = = = +, 3 = = 180, 2 = , = = = 140, = = = , = = 540
171 6 + + = 180, 6 = = 180, 7 = , = = = 140, = = 220, = = 320 基础达标演练 n 150 n = n 7:
172 : 2 3: n 90 n F F F 答案与提示 n n = 150 n = 12 n = n n - 3, n = 5 2 n n = 14 n = n = 2160 n = n : 360 = 7: 2 n = α β α + β = 180 β = 1 5 α β = = = n
173 n = n 120 n = 6 n n = 2880 n = = n 1 n 2 n : n = 3: 8 n 1 : n 2 = 1: 2 n 1 = 5 n 2 = n n = n 150 n = = x x - 90, x + x - 90 = x = 135 n 135 n = = 8 15 = = = = 108, = = 36 = = 36, - = = 72, F = F G F M F = = G G = + GM + G = GMF, GMF = + + FM + + F + GMF = 360, F = 360 难点指津 n 169
174 n n 3 2 n n - 1 n + 1 n 综合延伸 n n n n n x n = x, n - 2 = x 180 n = x 180 n, 60 + x < x <
175 , x = 120 n = n 1680 < n < < n < n, n = 12, n = n
176 n n n - 2 n - 1 n 思维拓展测试 n n 4 n :
177 = 60 = 135 F F = 105 F = 30 1 F 答案与提示 1 20 n - 3 n n - 3 n - 2 n - 2 = 6 n = 8 n = n = 180 n = n 3 n 3 n = n 40 n n x 0 < x < 180 n = x x = 180 n < x < 180 n, n = 9 x = n n n n n = 63 8 n = 9
178 , 9 8 n , = n = 120 n n = 6, 9 1 F F = 105 F = 30, F = F - F = = 45 2 F F = 45 = 135 = 60, = F - - = = 120, + = = 180, F = 20 F = 30, + = = = = = = 150 视野情境扫描 n 2 n n n
179 n n N N = n - 2 N 180 = n L uler 1707 ~ Goldbach 1690 ~ 1764 n n n 3 = 1 4 = 2 5 = 5 6 = 14 7 = 42 8 = = J Segner 1704 ~ n = 2 n n n - 1 n n - 10 n = n H Urban n + 1 = 4n - 6 n n 175
180 2 3 学习指导 1 2 知识点精析 n k n n - 2 k 180 n = 360 n - 2 k - 2 = 4 kn - 2k - 2n = 0 n = 2k k - 2 = k n k, k
181 , k = 3 n = = 6 k = 4 n = = 4 k = 6 n = = m x n y m n m m - 2 m 180 n n - 2 n 180 x m 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
182 问题探究
183 = = = = = = = = = 360, 解题方法指导
184 180
185 n n 6 + n = 4n + 2 4n m n 120m + 90n = 360 4m + 3n = 12 m n, 181
186 = = x y 60x + 150y = 360 2x + 5y = 12 x = y x y y = 2 x =
187 基础达标演练 獉獉獉 6 183
188 答案与提示 = m n 90 m n = 360 3m + 4n = 12, m = n n m m = 0-8, m = = 360 难点指津
189 综合延伸 6 m n m n m n m n 60m + 120n = 360 m n m n m n , 60m + 120n = 360 m + 2n = 6, m = 6-2n m n, n = 1 m = 4 m = 2 n = 2 m n n = = < 1620 < , x 150 y 120 x y = x + y = { x = 1 y =
190 ,
191 a = 思维拓展测试 1 a b b =
192 5 n n + 76 n n n n 2 y y 1 n n n m 3 5 m cm cm cm cm 2 答案与提示 a + 150b = 360 2a + 5b = 12 a = 6 - b = 2 a a = b = = = x x = 360 x = 90
193 4 5 a b a 2 n = b 2 n + 76 n a + b a - b = b 2 1 n a b a + b > a - b a - b = 1 a + b = 19 n = 4b 2 a = 10 b = 9 n = n + 3 n y = n + 3 n + 2 = n 2 + 5n y = 506 n + 3 n + 2 = 506 = 23 22, n = 20 4 n n + 1 = = = = n n + 1 = n 2 + 5n n n + 1 = 4n + 6 n 2 + n = 4n + 6 n 2-3n = 6 n n - 3 = n cm = = = 84, cm 2 84 视野情境扫描 = 100 = =
194 = = 121 = = = = = 144 = = = 936 n n + n 2 6 = 6n n
195 2 4 学习指导 知识点精析
196 解题方法指导
197 m n 60m + 160n = 360 m = 6-8 n 3 n m n = n =
198 n a a 3 = = 39 m 194
199 基础达标演练 m n 1 n 2 n 3 n m m m n 1 n 2 n 3 n m m 195
200 15 m 20 m 答案与提示 = = = = = = m n 120m + 135n = 360 m = 3 - m 9 8 n n 196
201 n n n n , n 1 n 2 n 3 n m n n n m n 2 n n n 3 + n n 2 1 n n n n m = m - 2 m n m + n n 3 n n m = n m = =
202 25 18 = 450, m m m 0 6 m = = 视野情境扫描 n n 5 n n
203 n s t u v s + t + u + v = n { 60s + 90t + 120u + 150v = n s + t + u + v = n 1 { 2s + 3t + 4u + 5v = 6n v 3s + 2t + u = 12 - n 0 n 12 1 n 1 2 s t u v
204 热点题型分析 n n = = = = a MN MN
205 1 8 x 2x x + 3a 2x = x + 3a x = 3a 30a 2 M N, M = N = 90 = 60, MN = = a = 360 热点考题训练 n 1080 n n = n n n
206 n 2 n n l l 3l 2l 2 3 l
207 x y x > y 獉獉獉 x + y = 7 x - y = 2 4xy + 4 = 49 x 2 + y 2 = n 2n 270 n F F = cm F = 3 = = = : 1 4:
208 答案与提示 , = 10, n = = n = 1080 n = n , = n = 16 n 2 4n = = , = = = = = = = 2 3 l 11 x + y 2 = 49 x + y = 7 x - y = 2 x = 9 2 y = 5 2 4xy + 4 = 49 n n = 270 n 2n 13 n = n = F F 1, F = F = 1 1 F 1 = 120, F = F, 1 = F 1 F = = 120, 1 = 204
209 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 = = = 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 = = x x, 2x x : 3 2x x 2x , 3 = 2x 10 5 x x 4 x = 5 2x = n < n < < n < n, n = n = = : 3:
210 m 7 n R R m - R n = F + G = FGHI 6 cm 9 10 m n m + n = 360 m = n = n n n 1999 n n n n
211 n + 1 2n + 2 2n + 1 2n = = = 2 3 = 4 5 = 6 7 = 8 + F = n n n F FG F + G + H FGH
212 n n n 3 74 答案与提示 = 270 2k 3k 4k 2k + 3k + 4k = 270 k = α β α + β = 180 β = 1 3 α β = = 8 n n n n = n = = 1080 n n = 27 n = = m - 3 = 7 m = 10 n = 3 R = 5, m - R n = = F + = G + G = = = 180, F + G =
213 8 2 cm FGHI, = F = FG = GH = HI = I F = FG = FGH = GHI = HI = I = 120 I F GH, F = FG = G = 1 3 = = 2 cm = = m 90 + n 135 = 360 m = 1 n = n n n = 100 n = < 1999 < < 1999 < , n = m m = 360 n m = 2n = 102 = = 540, + + = = 426 = =, = = 180 F = 180, + F = = 2 3 = 4 5 = 6 7 = 8, = = 180, + F = α n α = 2400 α = n < α < 180, 0 < n < 180 n - 2 { > 0 { n > 15 1 n < n < 16 1, < n < n 3, n =
214 21 G + H = HG + G + = +, F + G + H = + HG + G F + G = FG + G + F + F = F- G = F GH MNPQ , MNPQ P Q FMG NH GH = x H = y MQ = NP, MF + F + Q = N+ + P, 槡 槡 2 = 槡 2 2 y 槡 2, y = 3 - 槡 2 MN = QP, x = 槡 2, 32 + 槡 2 23 n α n α α = 600, α = 90n < α < 180, 0 < 90n < 180, < n < n, n
215 n 2 + n n 2 + n = 8n n - 6 = 74 n = 10 n 2n - 1 2n = 4n 2-2n n = 10 4n 2-2n = =
216 F = > > 读懂前面的材料再应用 是解这类题的关键 F 210
217 F 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 O F G H FGH, O = O O = O = 90 O = O , O O 2 OH OG Rt O Rt O 211
218 , OH = OG 3 OH = O = OF OH = O = OF = OG, G HF, FGH O OG OG ' ' ' ' = ' = + ' + ' + = 180 =
219 = 4 cm = 10 cm F = cm, = = x = 10 - x Rt 2 = x 2 = x 2 x = O F 1 F = F O = OF F F 2, = = F = F, - = - F, F = 213
220 , F = 5 = 40 = 45 3 F G F G H I IF J HF K HIKJ 2 F H I K J F 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 HIJK F, HG = K GI = J, HG: = GI: 214
221 >, GI > HG, K > J, F K J F J K H I F = x HG = = 45 = 5, = 5 = GI G = HG = 5-2x = GI, G: = GI:, 5-2x : 5 = 5: 40 ( ), x = 1, F = 5 - x = 4 F, 5 2 F G G G GF G H 1 1 G 2H 215
222 2 G H G = G 1 2 H = G 1 1 GF, = G = G = = 90, G 2 G, G = G = GH, G - G = GH -, HG = G = 90 H 2 H = = = 1, = 槡 2, = - = 槡 2-1, G = = 槡 2-1 G = 槡 2-1 H Rt PMN P = 90 PM = PN MN = 8 cm 8 cm 2 cm M MN Rt PMN MN 1 cm N x PMN y cm 2 y x 216
223 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 PM Rt M = = x, y = 1 2 M = 1 2 x2 0 x F T 2 < x MG M = x MF = 2, F = G = x - 2 = 2 217
224 , y = 1 M + G = 2x < x T N 6 < x PN Q MQHG M = x, N = Q = 8 - x = 2, y = 1 MN + GH N Q = - 1 x < x F F F P
225 = 90 F = = 2 = 90 = 30 F = 90 = 2 F = = > G = G F G F F
226 > G H H HF = G F > G = G F G F F a FGH G N 1 N 2S + S FGH = S N 1 a b a > b FGH M M M MN M N MN N N 1 MN a b MN FGH MN n n
227 1 MN M Rt 2 = MN a b N NP MN Rt M Rt = M + M = + M = 90, M =, Rt M Rt, M =, MN a 2 + b 2 2 = = a 2 + b 2, MN 2 N NP P MN 2 n n = 8 = S 1 S 3 S 1 = S 2 = S 3 = S 2 221
228 O 3 1 S = S + S = 1 2 O O S = = O 24, S = 1 2 O S = 1 2 O = 24, S = 1 2 O O = 1 2 O + O = = m 222
229 m n m m m m n n m 223
230 m m m m 3 m m 4 m n m 224
231 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 i i = h l 1: m 1 M F FN N MN = F N N FN N = i 1 i 2 1 F FN N MN = F = 7 75 m FN = M = 3 m i 2 = FN N, N = 5 1 m, M = MN + N = = m 2 i 1 = M M, M = h i 1 N = h i 2 = M - M = MN + N - M = h i 2 -, S = 1 F + M 2 = h h 2 ( - i 2 i ) h S = 1 2 ( ) h i 2 + h i 1 1 h h i
232 獉獉 360 獉獉 x y 60 x y = 360 x +2y =6 x y x = 2 y = 2 x = 4 y = x y 獉 獉獉獉獉 x y x y 60 x + 90 y =
233 2x + 3y = 12, x = y x y, y = 2 x = 综合训练题 F F 8 F 22 F a b c d b
234 1 b a b c d V 7 9 F M N MN P Q PQ = n n F = 50 F = F
235 = = = 90 = 25 = FGH 1 m S x S x S = S x S x S = 3 n S x 229
236 S =
237 F ' ' F = 65 ' = 6 F F = F 槡 3 2 槡 3 3 槡 3 槡 F F F ' = 4 ' = 槡 槡 FG = 槡 3 2 槡 槡 3 F G F F F F V 1 ' ' F 2 = 63 ' F
238 F = F F F = = = = = 45 F F F F F F F 1 = F 2 F x cm 10 cm 80 cm x 232
239 GF G 1 G 2 G F G G 1 F 2 F G F O M N G F G F OFG O O OFG O 1 G 2 a OMN :
240 獉獉獉 獉獉獉
241 獉獉獉 F m n S 1 S S 1 S 2 < = >
242 S 1 S 2 n S 1 S 2 < = > m 3 2 m 2 m i = 1: 2 i' = 1: 2 5 H H 1 25 M m 6 m N G F 1 2 F F 1 = 10 8 = F = F F 236
243 2 F F F M M F F F F 2 N N F N N = F F 237
244 N F M 1 F M 2 O G F O F F = F G OG 1 F 2 OG F 3 G G = 4-2 槡 = 5 cm = 6 cm = 60 = 90 MPN N a cm MN l N = 8 cm a 2 cm 2 a 3 P 2 1 l M N
245 n n n n O O O x y 1 O O x ' 2 O = 2 槡 5 O: O= 1: cm = 60 P Q P P Q 4 cm/s 5 cm/s 12 s P Q M N MN P Q M N P Q a cm/s 3 s P Q F F 2 MN a F P PF Q y Q
246 Q Q Q Q cm Q Q Q Q Q Q 2 1 Q Q 3 1 Q Q P F F 1 Q = 8 = 6 P P = x P y 1 y x x 2 P P P = O F F G G 1 FOG 2O 2 O F = G FOG 2O 240 P
247 = 10 = 60 M 1 M t 0 t 10 1 N M MN N M P 2 N M NM 3 N M a a 2 M MP P MPN MPN S t S S = 0 a y x = 3 = 5 2 x P 1 - O - - P P 2 P t 1 t = 5 P 2 OP S S t t 答案与提示 1 7 F = F = F + + F = 8 F + =8 + F + F =22 + =15 - F =7 F =7 2 1 a c d V+ F - = x
248 3 30 P P PQ = 1 P = n n n = F = = 50 F = = 80 6 P Q PQ O O 7 30 = = 25 = 24 = 90 = 7 F F F = = 24 F = - F = - = 18 = = x x x + n ' F = F = F = 65 F = 115, ' = ' F = = = F = F = 30 = F = 6 = 90 = 3槡 3 15 = ' = 30 = 90, = 2 = 8 16 ' M ' M ' M = M ' = ' M = ' = 30 = 90 = 槡 3 = 2 242
249 F, F = = 63 ' ' F F, ' F = F = 63, ' F = ' F - F = F 2 F = , =, =, = F = F, F, = F 19 1 = = =, 2 = = = = 90 = = 90 = = = = 90 =, F, =, =90, =90, 20 = = F F Rt F F = 45, F = F, Rt F Rt F { F = F F = F = 90 F = F, F F S, = 21 = F F F, = = F = F = } Rt Rt F F F
250 , = F 22 1, = =, = F, = F = 90 =, F S, = F 2 F 23 2 x + 10 cm 10x 2 2 x + 10 < 80 { 10x > 100 x < 30 { x > 10, x 10 < x < = G GF, = = G, = G = 90, G, = G 2 1 Rt Rt G Rt 90 Rt G Rt G 90 Rt 25 1, 1 = = = F, = 1 2 F = 1 2, = F, F 2 F G, G, G F, = =, = =, = = = 180, = 180, + = 90 = 90, G 26 1 = G O O O, O = O O = 90, O = OG OFG, O = OG, 244
251 O OG, = G 2 OMN 1 OMN 4 a
252 F S 1 < S 2 S 1 = S 2 S 1 > S
253 S 1 < S 2 S 1 = S 2 S 1 > S 2 3 l l l l S 1 S 2 S 1 < S 2 S 1 > S 2 S 1 > S 2 S 1 < S 2 S 1 = S 2 33 a b h F S F = a + b S F = h a b = 1 a + b 2 S a + b = S = h =, S = S S = S, S + S = S + S, F G = 3 2 m , MN = F = 5 2 m M = NF = 6 m Rt HMN Rt F MN HN = F F = 1 2, HN = 2 5 MN = 13 m F = 2F = 10 4 m, H = HN + NF + F = = 29 4 m H 29 4 m 247
254 35 1 = 10 8, S = 80 = F = F, S = 1 4 S S F = 1 8 S S F = 1 4 S S F = S - S - S F - S F = 3 8 S = = x y S F = 4 F x ( ) 8 F y - x, S = 1 F 2 y - 8 x 6x xy - 8 x xy - 14 = S xy - 8 = 1 2 y = = 0 xy = 20 4 = 3, = 6x xy - 8 = x - x xy - 14 y = 5 xy 2-24xy + xy - 8 S = xy > S = 5, xy = 4, xy = 20 S F = S - S - S F - S F = = O 12 2 O O O O O O=10 O =60, O =30, O =2O=20, =10 槡 3, 20 槡 3 cm = 2 = = 360, 3 1 = = 120 F 1, N 3 2 F MN FMN = FNM = = 30 2 M H 248
255 HMN = 30 HNM = 90, NH = 1 2 MH = F 2N = F N, N = F M N =, N = F = = 135 N + = 90 F + = 90, N = F, N F, = F N = F 2 N = N = N N N = F = F 39 1 = = 90 F = = 90 F =, F 2 OG = 1 F 2 F = F = G, G = = 90 G F G = G, GF G, = F G F O, O, OG = 1 2 F 3 = x = x = 槡 2x 2 F = = 槡 2x, F = F - = 槡 2-1 x Rt F F 2 = 2 + F 2 = x 2 + 槡 x 2 1 G = G = G G = G = 90, G G, G 2 = G G = 4-2 槡 2 G G = G G F = 2G, F 2 = 4G 2 = 槡 x 2 + 槡 x 2 = 槡 2 x 2 = 4
256 , MN 1 MN 1 1 = 10 N = 8 N 1 = 2 1 N 槡 3 S M1 N = 槡 3 = 槡 3 槡 3 cm 2 P l 1 M 2 1 M N PMN a PM = = = 60 P l M 2 N , = 30, = 1 = 3 2, = 3 槡 3 = 2 2 = 3 槡 3 PMN = M=90, M 2 2 = 30 M 2 = 3, MN = M N = =10 a 10 cm PM 3 1 F FM 1 = 1 2 S 槡 3 = 21 2 槡 3, S FMN = 21 4 槡 3 l 2 3 P 3 F S FM1 1 2 M 1 N S =
257 M 1 = x M 1 槡 3 2 x, 1 2 x 槡 3 2 x = 21 4 槡 3, x = 槡 21 1 N = 2, MN = M N = 槡 槡 cm n 251 x > ' 3 ' F' OF' 2 Rt O O = 90 O: O = 1: 2 O 5k 2 = 20 O = k O= 2k 2 = O 2 + O 2 k > 0, k = 2, O = 2 O= 4, = x = x O = 4 - x Rt O 2 = O 2 + y P 1 2 F O 2 x 2 = x 2 x = 5 2 = 5 2 F F S F = 1 2 O = 1 2 F 5 2 F 槡 = = 60 x 2 = 2 槡 5 F = 槡 5 P,, = 24 cm N 2 MN F M 12s P M 4 12 = 48 cm F Q + = 48 cm, M Q N 5 12 = 60 cm F
258 + + 1 = 60 cm, N 2 MN M = M N = N, MN, MN 3 P M 3s 4 3 = 12 cm 1 2 = 12 cm, Q N 3s 3a cm F 2 Rt MN F = = 60 1 F = NM = 90 Ⅰ F N F = N - FN = 12-3a Rt F F = 30, F = 1 2, 12-3a = a = 2 Ⅱ F F = 3a - N = 3a - 12 Rt F F = 30, F = 1 2, 3a - 12 = a = 6 2 F = NM = 90 F 3a = N + = 36, a = 12 a = Q Q Q Q Q = 3Q Q = 3Q Q = 3Q 2,, PF QF, P Q = F F 252
259 , P F, Q = 2 P = 2 Q = 4, 3 Q Q = 3 Q = 3Q P P P, P P = P = 10 P = - P = 10 - x P 8 = 10 - x 10 P = x, P = 1 12 P = x P = P = x y = x x 0 < x < P = 12 5 x P P P = 24 = =, = = =,, 1 = 2 G, 2 = 3, 1 = 3, G = G G O F O, GOF, G = OF F = OG, GOF = 2 OG + G = 2 OG + G = 2O 253
260 G 1 3 O F 1 2 G O O F G F O F F G G FOG 2O O F F G G FOG 2O MN N M MN MN 2 N 2 M 1 N M N NM t = 10 2 =5 M=5 1 =5 N = =10 75 = 槡 3 5 = 60 = 5 槡 3 254, S NM = 1 2 M + N = 槡 3 M F MPN MP = 10 PN = = 10 MP = PN, N = PN - P = - P = P P = M = t G P N
261 , P = 10 - t N = t P PG G Rt PG PG = = 60, PG = 槡 t 2 MN F MP = PN, NF = NMP = MNP, F = N = t MPF, S = 1 2 t + 10 槡 t = - 槡 3 4 t 槡 3 S = 0 - 槡 3 4 t 槡 3 = 0 t 1 = 10 t 2 = - 10 N = at N = PN + P = 10 + t, at = 10 + t t = 10 at = 10 + t a = P = = t = 5 P O= 10 + P = 5, P = 2 P P P = = 3 = P = 2, O = O+ = = 12, P Ⅰ 0 < t 3 P O=2t P = t, s = 1 2 2t t = t2 Ⅱ 3 < t 8 P O= 2t, s = 1 2 2t 3 = 3t Ⅲ 8 < t < 11 P O= 2t + + P = t, P = P = 11 - t, s = 1 2 2t 11 - t = - t2 + 11t s t 0 < t 3 s = t 2 3 < t 8 s = 3t 8 < t < 11 s = - t t 255
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