八年级数学
（测试内容：第一章 轴对称图形）
班别 座号 姓名 成绩
说明：1．可以使用计算器，但未注明精确度的计算问题不得采取近似计算，建议根据题型特点把握好使用计算器的时机．
2．本试卷满分100分，在90分钟内完成．相信你一定会有出色的表现！
一、填空题：本大题共10小题；每小题3分，共30分．请将答案填写在题中的横线上．
1．如果两个图形关于某一条直线对称，那么连结对称点的线段被________________垂直平分.
2．如图，是一个轴对称图形,对称轴为直线l.图中A、D、E关于直线l的对称点分别是___________,图中长度相等的线段是_____________________ ________________________________________.
3．到线段的两个端点的距离相等的点有_______个，一条线段的垂直平分线有_________条.
4．如果一个等腰三角形的一个外角等于40°，则该等腰三角形的底角的度数是 ．
5．在等边三角形ABC中，AD是BC上的高，则∠BAD＝ ．
6．等边三角形的两条高线相交所成的钝角的度数是
．
7．在镜中看到的一串数字是“
”，则这串数字是
．
8．如图，AB＝AC，∠1＝∠2，BD＝3cm,那么BC的长为 cm．
9．如图，等边三角形ABC的三条中线交于点O.则图中除△ABC还
有____________________________________________是等腰三角形．
10．如图，在等腰梯形ABCD中，对角线AC与BD交于点O，图中全等的三角形是
．
二、选择题：本大题共8小题；每小题3分，共24分．在每小题给出的四个选项中，只有一项是正确的，请将正确答案前的字母填入题后的括号内．每小题选对得3分，选错，不选或多选均得零分．
11．····························································································································································· 下列是我国四大银行的商标，其中不是轴对称图形的是····················································································································· （ ）．
 |
（A） （B） （C） （D）
12．····························································································································································· 下列图形不一定是轴对称图形的是····························································································································································· （ ）．
（A）线段 （B）正方形 （C）半圆 （D）三角形
13．····························································································································································· 正五角星的对称轴有 （ ）．
（A）1条 （B）2条 （C）5条 （D）10条
14．····························································································································································· 已知△ABC的周长为24，AB＝AC，AD⊥BC于D，若△ABD的周长为20，则AD的长为···················································· （ ）．
（A）6 （B）8 （C）10 （D）12
15．····························································································································································· 已知等腰三角形的一边等于3，一边等于6，那么它的周长等于········································································································ （ ）．
（A）12 （B）12或15 （C）15 （D）15或18
16．····························································································································································· 已知等腰三角形的周长为24，腰长为x，则x的取值范围是··············································································································· （ ）．
（A）x＞12 （B）x＜6 （C）6＜x＜12 （D）0＜x＜12
17．·············································································································· 如图，等边三角形ABC中，AD是BC上的高，取AC的中点E，连结DE，则图中与DE相等的线段有····················· （ ）．
（A）1条 （B）2条
（C）3条 （D）4条
18．·············································································································· 如图，在△ABC中，点O是∠ABC的平分线与线段BC的垂直平分线的交点，则下列结论不一定成立的是·········· （ ）．
（A）OB＝OC （B）OD＝OF
（C）OA＝OB＝OC （D）BD＝DC
三、解答题：本大题共4小题，共46分．解答应写出文字说明或演算步骤．
19．（10分）（1）请仔细观察图形（阴影部分），指出所给虚线中哪些是图形的对称轴？
（2）下列图形是轴对称图形吗？如果是，分别画出它们的对称轴.
20．（12分）（1）在数学课上，老师提出了一个问题：“角是轴对称图形吗？如果是，那么它的对称轴是什么？”小明同学马上举手回答：“角是轴对称图形，角平分线就是它的对称轴．”同学们，小明同学的回答有正确吗？为什么？
（2）如图，在△
中，∠C＝90°，用刻度尺及量角器分别作出AC、BC边的垂直平分线，并说明它们的交点与斜边AB的关系．
21．（12分）（1）如图，已知AD是线段BC的垂直平分线，且BD＝3cm，△ABC的周长为20cm，求AC的长．
（2）如图，在△ABC中，AB＝AC，AD⊥BC，∠BAD＝40°，AD＝AE．求∠CDE的度数．
22．（12分）已知：如图，在等腰梯形ABCD中，AD∥BC，AC⊥BD，垂足为O，AC＝8cm.求梯形ABCD的面积.
八年级数学参考答案
一、填空题：（每小题3分，共30分）
1．对称轴；2．B、C、E，CE＝DE,CF＝DF,AC＝BD,AF＝BF；3．无数，且只有1；4．20°；
5．30°；6．120°；7．309087；8．6；9．△AOB、△AOC、△BOC；10．△ABC≌△DCB、△ABD≌△DCA、△ABO≌△DCO．
二、选择题：（每小题3分，共24分）
| 题号 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| 答案 | A | D | C | B | C | C | D | C |
三、解答题：
19．解：（1）d；（2）都是轴对称图形，作图略.
20．解：（1）有错误的地方，错误出现在“角平分线就是角的对称轴”因为对称轴是一条直线，而角平分线是一条射线．对称轴应该说是角平分线所在的直线；
（2）作图略，AC、BC边的垂直平分线的交点恰好是斜边AB的中点．
21．解：（1）7cm；（2）20°．
22．解：32cm2.
提示：梯形ABCD的面积＝△ACD和面积＋△ACB的面积
＝
×AC×OD＋×AC×OB
＝×AC×（OD＋OB）
＝×AC×DB＝32cm2；
或将对角线AC平移到DE，交BC的延长线于E，于是得△DCE≌△BAD，所以△BDE的面积等于梯形ABCD的面积.