第2课时 作轴对称图形的对称轴
01 基础题
知识点1 线段的垂直平分线的画法
1．下图的尺规作图是作(A)
A．线段的垂直平分线 B．一个半径定值的圆 C．一条直线的平行线 D．一个角等于已知角
![](https://wkrtcs.bdimg.com/rtcs/image?w=70.00&md5sum=44c01f12d6b5df98c69cc10677149c3c&sign=663fd02598&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=549&ipr={"t":"img","r":"r_4","w":"70.00","h":"89.00","dataType":"png","c":"word/media/image2.png","imgOriW":437,"imgOriH":557})
2．如图,△ABC中,AB＝6,AC＝4,分别以点B和点C为圆心,以大于BC一半的长为半径画弧,两弧相交于点M和N,作直线MN,直线MN交AB于点D,连接CD,则△ADC的周长为10．
![](https://wkrtcs.bdimg.com/rtcs/image?w=69.00&md5sum=44c01f12d6b5df98c69cc10677149c3c&sign=663fd02598&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=549&ipr={"t":"img","r":"r_4","w":"69.00","h":"86.00","dataType":"png","c":"word/media/image3.png","imgOriW":432,"imgOriH":540})
3．如图,在某河道l的同侧有两个村庄A,B,现要在河道上建一个水泵站,这个水泵站建在什么位置,能使两个村庄到水泵站的距离相等？
![](https://wkrtcs.bdimg.com/rtcs/image?w=91.00&md5sum=44c01f12d6b5df98c69cc10677149c3c&sign=663fd02598&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=549&ipr={"t":"img","r":"r_4","w":"91.00","h":"62.00","dataType":"png","c":"word/media/image4.png","imgOriW":209,"imgOriH":142})
解：连接AB,作线段AB的垂直平分线,与直线l的交点即为所求作的点．如图．
知识点2 作对称轴
4．指出下列轴对称图形各有几条对称轴,并把它们画出来．
![](https://wkrtcs.bdimg.com/rtcs/image?w=306.00&md5sum=44c01f12d6b5df98c69cc10677149c3c&sign=663fd02598&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=549&ipr={"t":"img","r":"r_4","w":"306.00","h":"76.00","dataType":"png","c":"word/media/image5.png","imgOriW":702,"imgOriH":174})
解：4个图形对称轴的条数分别为：一条、两条、两条、四条．如图．
5．(抚州中考)如图,△ABC与△DEF关于直线l对称,请仅用无刻度的直尺,在下面两个图中分别作出直线l.
![](https://wkrtcs.bdimg.com/rtcs/image?w=220.00&md5sum=44c01f12d6b5df98c69cc10677149c3c&sign=663fd02598&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=549&ipr={"t":"img","r":"r_4","w":"220.00","h":"99.00","dataType":"png","c":"word/media/image6.png","imgOriW":505,"imgOriH":227})
解：如图所示．
02 中档题
6．(德州中考)如图,在△ABC中,∠B＝55°,∠C＝30°,分别以点A和点C为圆心,大于![](https://wkrtcs.bdimg.com/rtcs/image?w=22&md5sum=44c01f12d6b5df98c69cc10677149c3c&sign=663fd02598&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=549&ipr={"t":"img","w":"22","h":"43","c":"df4344a8d214cca83c5817f341d32b3d.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=113.00&md5sum=44c01f12d6b5df98c69cc10677149c3c&sign=663fd02598&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=549&ipr={"t":"img","r":"r_4","w":"113.00","h":"66.00","dataType":"png","c":"word/media/image7.png","imgOriW":707,"imgOriH":415})
A．65°
B．60°
C．55°
D．45°
7．如图,AO,BO是两条笔直的交叉公路,M,N是两个村庄,现准备建一个联通信号塔,要求信号塔到两个村庄的距离相等,并且到两条公路的距离也相等,同时在∠AOB所在区域内．则信号塔应修在什么位置？在图中标出塔的位置．
![](https://wkrtcs.bdimg.com/rtcs/image?w=99.00&md5sum=44c01f12d6b5df98c69cc10677149c3c&sign=663fd02598&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=549&ipr={"t":"img","r":"r_4","w":"99.00","h":"93.00","dataType":"png","c":"word/media/image8.png","imgOriW":621,"imgOriH":582})
解：∠AOB的平分线与线段MN的垂直平分线的交点即为塔的位置,图略．
03 综合题
8．如图,△ABC和△A′B′C′关于直线MN对称,△A′B′C′和△A″B″C″关于直线EF对称．
![](https://wkrtcs.bdimg.com/rtcs/image?w=110.00&md5sum=44c01f12d6b5df98c69cc10677149c3c&sign=663fd02598&rtcs_flag=1&rtcs_ver=4&l=webapp&bucketNum=549&ipr={"t":"img","r":"r_4","w":"110.00","h":"107.00","dataType":"png","c":"word/media/image9.png","imgOriW":252,"imgOriH":245})
(1)画出直线EF；
(2)直线MN与EF相交于点O,试探究∠BOB″与直线MN,EF所夹锐角α的数量关系．
解：(1)如图所示．
(2)∵△ABC和△A′B′C′关于直线MN对称,
∴∠BOM＝∠B′OM.
又∵△A′B′C′和△A″B″C″关于直线EF对称,
∴∠B′OE＝∠B″OE.
∴∠BOB″＝∠BOM＋∠B′OM＋∠B′OE＋∠B″OE＝2(∠B′OM＋∠B′OE)＝2α,
即∠BOB″＝2α.
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