（福建南平）2020-2021学年第一学期八年级期中测试-数学试题卷（人教版）参考答案及评分建议

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2020-2021 学年第一学期八年级期中测试-数学试题卷
参考答案及评分建议
一、选择题：本题共 10 小题，每小题 4分，共 40 分．
1
2
3
4
5
6
7
8
9
10
B
C
A
C
D
B
A
D
C
D
二、填空题：本题共 6小题，每小题 4分，共 24 分．
11．九 12．20°
13．15 14．16
15．= 16．8
三、解答题：本题共 9小题，共 86 分．
17．（本小题满分 8分）
证明：∵∠BAD=∠CAE，
∴∠BAD+∠DAC=∠CAE+∠DAC，
即∠BAC=∠DAE． ············································································· 2 分
在△ABC 和△ADE 中，
BAC DAE
AB AD
BD
 
 
， ············································································· 5 分
∴△ABC≌△ADE(ASA)． ···································································· 6 分
∴BC=DE． ······················································································· 8 分
18．（本小题满分 8分）
解：（1）如图，△A′B′C′即为所求．
···························································· 5 分
（2）A′(2，3) B′(3，1) C′(－1，－2) ························································ 8 分
19．（本小题满分 8分）
证明：∵AD⊥BC，
∴∠BDF=∠ADC=90°． ······································································· 2 分
∵∠ABC=45°，
∴∠BAD=∠ABC=45°，
∴BD=AD． ······················································································· 4 分
∵AD⊥BC，BE⊥AC，
∴∠C+∠DAC=90°，∠C+∠CBE=90°，
八年级数学参考答案第 2页（共 6页）
∴∠CBE=∠DAC． ············································································· 6 分
在△BDF 和△ADC 中，
CBE DAC
BD AD
BDF ADC
 
 
， ············································································ 7 分
∴△BDF≌△ADC(ASA)． ···································································· 8 分
20．（本小题满分 8分）
证明：∵AD 是∠BAC 的平分线，DE⊥AB，DF⊥AC，
∴DE=DF，∠AED=∠AFD=90°，∠EAD=∠FAD，
∴点 D在EF 的垂直平分线上． ····························································· 2 分
在△AED 和△AFD 中，
AED AFD
EAD FAD
AD AD
 
 
，
∴△AED≌△AFD(AAS)， ···································································· 4 分
∴AE=AF，
∴点 A在EF 的垂直平分线上， ····························································· 6 分
∴AD 所在直线是 EF 的垂直平分线，
即AD 垂直平分 EF． ··········································································· 8 分
21．（本小题满分 8分）
解：（1）如图，DE 所在直线是 AC 的垂直平分线．
························································ 3 分
（2）如上图，连接 AD．
∵AB=AC，∠BAC=120°
，
∴∠C=∠B=30°
． ············································································ 4 分
由（1）知，DE 所在直线是 AC 的垂直平分线，
∴AD=CD， ···················································································· 5 分
∴∠DAC=∠C=30°
，
∴AD=CD=2DE，∠BAD=120°
－30°=90°
， ············································ 6 分
∴△ABD 是直角三角形，且∠B=30°
，
∴BD=2AD=4DE．
∵DE=2 cm，
∴CD=4 cm，BD=8 cm，
∴BC=BD+CD=12 cm，
即BC 的长为 12 cm． ······································································· 8 分
（福建南平）2020-2021学年第一学期八年级期中测试-数学试题卷（人教版）参考答案及评分建议.pdf

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作者：envi 分类：初中 价格：3知币 属性：6 页 大小：336.31KB 格式：PDF 时间：2025-04-24

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