2016~2017年武昌区八年级上学期期中(附答案)

2016~2017年武昌区八年级上学期期中(附答案)
2016~2017年武昌区八年级上学期期中(附答案)

第1题

第4

题2016-2017第一学年度部分学校八年级期中联合测试

数学试卷 姓名:

考试时间:120分钟 试卷满分:120分

一、选择题(每题3分)

1.图中共有三角形的个数为( ) A. 4 B. 5 C. 6 D.7

2.下列长度的三条线段能组成三角形的是( ) A.1,2,3 B.4,5,10 C.8,15,20 D.5,8,15

3.若一个三角形的两边长度分别为2和4,则第三条边长可能是( ) A. 2 B. 4 C. 6 D. 8

4.如图,在△ABC 中,CD 是∠ACB 的角平分线,∠A=80°,∠ACB=60°,则∠BDC 为( ) A. 80° B. 90° C. 100° D. 110°

5.一个多边形的内角和是外角和的2倍,则这个多边形的边数为( )

A. 4

B. 5

C. 6

D. 7 6.凸八边形共有对角线的条数是( )

A. 20

B. 40

C. 28

D. 56

7.如图,直线a ∥b ,直角三角形如图放置,∠BCD=90°,∠1+∠B=70°,则∠2的度数为( ) A. 20° B. 25° C. 35° D. 40°

8.如图,∠ABD 与∠ACD 的角平分线交于点P ,若∠A=50°,∠D=10°,则∠P 的度数为( ) A. 15° B. 20° C. 25° D. 30° 9.如图在△ABC 中,∠BAC=60°,AD 平分∠BAC 交BC 于点D ,若AB=AC+CD ,则∠ADB 的度数为( ) A. 100° B. 110° C. 120° D. 130°

10.如图,在△ABC 中,点M 、N 是∠ABC 与∠ACB 三等分线的交点,若∠A=60°,则∠BMN 的度数为( ) A. 45° B. 50° C. 60° D. 65°

第10题

第9题

第8题

第7题

D

二、填空题(每题3分)

11.点P (-3,2)关于y 轴对称点M 的坐标为 .

12.如图,已知CE 平分∠ACB ,且CE ⊥DB ,∠DAB=∠DBA ,若AC=18,△CDB 的周长为28,则BD 的长为 .

13.如图,△ABC 的顶点均在坐标轴上,AD ⊥BC 于E ,交y 轴于点D ,已知B 、C 的坐标分别为B (0,3)C (1,0),若AD=BC ,则△ABC 的面积为 . 14.将一副三角板如图放置,使含30°角的三角形的短直角边和含45°角的三角板一条直角边重合,则∠1的度数为 .

15.如图,在△ABC 中,AB=AC ,D 、E 是△ABC 内两点,AD 平分∠BAC ,∠EBC=∠E=60°,若BE=6cm ,DE=2cm ,则BC= cm.

第17题

第19题

B 16.已知△AB

C 是等腰三角形,由点A 作BC 边上的高恰好等于BC 的一半,则∠BAC 的度数为 . 三、解答题

17.(本题满分8分)如图AE=BD ,AC=DF ,BC=EF ,求证:△ABC ≌△DEF

18.(本题满分8分)等腰三角形一腰上的中线把这个等腰三角形的周长分成21和24两部分,求这个等腰三角形各边的长. 19.(本题满分8分)如图,在△ABC 中,∠BAC=90°,AD ⊥BC ,BE 平分∠ABC ,G 为EF 的中点,求证:AG ⊥EF.

20. (本题满分8分)如图,在所给的网格图中,完成下列各题(用直尺画图,否则不给分) (1)画出格点△ABC 关于直线DE 的对称的111C B A △;

(2)在DE 上画出点P ,使PA+PC 最小; (3)在DE 上画出点Q ,使QA-QB 最大.

21.(本题满分8分)如图在△ABC 中,AB=BC ,M 、N 为BC 上两点,且∠BAM=∠CAN ,

MN=AN ,求∠MAC 的度数

第15题第14题

第23题

B

22.(本题满分10分)在△ABC中,∠B=110°,∠C的平分线交AB于E,在AC上取点D,使得∠CBD=40°. (1)求证:点E到AC和BD的距离相等;

(2)连接ED,求∠CED的度数.

23.(本题满分10分)如图在△ABC中,AD为BC边上的中线,E是线段AD上一点,且

1

2

AE BC

,BE的延长线交AC于F,若AF=EF.

求证:(1)AC=BE (2)∠ADC=60°

24.(本题满分12分)如图△AOB和△ACD是等边三角形,其中AB⊥x轴于E点.

(1)如图,若OC=5,求BD的长度;

(2)设BD交x轴于点F,求证:∠OFA=∠DFA;

(3)如图,若正△AOB的边长为4,点C为x轴上一动点,以AC为边在直线AC下方作正△ACD,连接ED,求ED的最小值

第22

A

一、 选自题(每小题3分,共计30分)

二、 填空题(每小题3分,共计18分)

三、解答题

17.证明:∵AG+EB=BD+EB

∴AB=DE…………………………………………………………………………………………………3分 在△ACB 和△DFE 中

AB DE AC DF BC EF =??

=??=?

∴△ABC ≌DEF (SSS )…………………………………………………………………………………8分 18.解:设底边长为a ,腰长为b

依题意可列方程组212422

2421

2

2b b a a b b b b ??+=+=????????+=+=????或………………………………………………5分

解得:1317

1614

a a

b b ==???

?

==??或…………………………………………………………………………………7分 又当a=13,b=16,满足b+b=32>13,可构成三角形 当a=17,b=14,满足b+b=28>17,可构成三角形

则该三角形三边长为13、16、16或者17、14、14……………………………………………8分 19.证明:∵BE 平分∠ABC

∴∠ABE=∠CBE ∠AEF=90°-∠ABE

又∵ ∠AFE=∠DFB=90°-∠CBE

∴∠AFE=∠AEF △AFE 为等腰三角形 又∵G 为EF 的中点 ∴AG ⊥EF

(若AG=AG ,FG=GE ,∠AFG=∠AEG ,则△AFG ≌△AEG 不给分) 20.(1)图略

(2)连1AC 或连1AC 得P 点即可 (3)连AB 交DE 于点Q 21.解:设BAM CAN α∠=∠=

∵MN=AN ,不妨设AMN MAN β∠=∠= 又∵AB=BC ,∴2C αβ∠=+ 在△AMC 中,()2180ββααβ++++=?

则60αβ+=? 所以60MAC ∠=?

22.解(1)延长CB 至点M ,

∵18011070ABM ∠=?-?=? ABM ABD ∠=∠ ∴点E 到CM 和BD 得距离相等 又∵CE 平分平分∠ACB ∴E 点到AC 和BC 的距离相等

∴点E 到AC 和BC 的距离相等……………………………………………………………5分 (2)∵CE 平分ACB ∠

∴设EBD EDA α∠=∠= ACE BCE β∠=∠= 又∵在△BDC 中,2240αβ=+? ∴20αβ-=? 在△EDC 中,CED αβ=+∠ 则20CED αβ∠=-=? 23.证明:(1)倍长AD 至点T ,连BT

可证:△ACD ≌△TBD ,得:AC=BT CAD T ∠=∠ 又∵AF=EF ,∴CAD AEF BET ∠=∠=∠

∴BT=BE ∴BE=AC………………………………………………………………………………5分 (2) 在DT 上取DM=DC ∴AE+ED=ED+DM 即AD=EM ∴△DAC ≌△MEB (SAS ) ∴BM=CD=BD

∴△BDM 为正三角形 60ADC BDM ∠=∠=?………………………10分 24.(1)证△OAC ≌△BAD

∴BD=OC=5…………………………………………………………………………………………………………3分

(2)由(1)得:AOF ABD ∠=∠

作AH ⊥BD 于点H 则△AOE ≌ABH ∴AE=AH

∠OFA=∠DFA………………………………………………………………………………………………7分

(3)连接DB 并延长至点N 易证:△AOC ≌△ABD (SAS ) ∴∠AOE=30°=∠ABN 则D 点在直线BN 上运动

过E 作EH ⊥DN 于点H ,当D 点运动至H 时,ED 最小 此时,1

12

EH BE ==……………………………12分

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