北师大版八年级下册《第1章 三角形的证明》单元检测卷A（一）

1、北师大版八年级下册第1章 三角形的证明2014年单元检测卷a（一）一、选择题（每小题4分，共48分）1等腰三角形的一个角是80，则它顶角的度数是（）a80b80或20c80或50d20显示解析2下列命题的逆命题是真命题的是（）a如果a0，b0，则a+b0b直角都相等c两直线平行，同位角相等d若a=6，则|a|=|b|显示解析3abc中，a：b：c=1：2：3，最小边bc=4cm，最长边ab的长是（）a5cmb6cmc7cmd8cm显示解析4如图，已知ae=cf，afd=ceb，那么添加下列一个条件后，仍无法判定adfcbe的是（）aa=cbad=cbcbe=dfdadbc显示解析5如图，在ab

2、c中，b=30，bc的垂直平分线交ab于e，垂足为d若ed=5，则ce的长为（）a10b8c5d2.5显示解析6如图，d为abc内一点，cd平分acb，becd，垂足为d，交ac于点e，a=abe若ac=5，bc=3，则bd的长为（）a2.5b1.5c2d1显示解析7如图，ab=ac，beac于点e，cfab于点f，be、cf相交于点d，则abeacf；bdfcde；点d在bac的平分线上以上结论正确的是（）abcd显示解析8如图所示，abbc，dcbc，e是bc上一点，bae=dec=60，ab=3，ce=4，则ad等于（）a10b12c24d48显示解析9如图所示，在abc中，ab=ac，

3、d、e是abc内两点，ad平分bacebc=e=60，若be=6，de=2，则bc的长度是（）a6b8c9d10显示解析10如图，在abc中，c=90，b=30，以a为圆心，任意长为半径画弧分别交ab、ac于点m和n，再分别以m、n为圆心，大于12mn的长为半径画弧，两弧交于点p，连结ap并延长交bc于点d，则下列说法中正确的个数是（）ad是bac的平分线；adc=60；点d在ab的中垂线上；sdac：sabc=1：3a1b2c3d4显示解析11如图，在平面直角坐标系xoy中，a（0，2），b（0，6），动点c在直线y=x上若以a、b、c三点为顶点的三角形是等腰三角形，则点c的个数是（）a2b

4、3c4d5显示解析12如图，在等腰rtabc中，c=90，ac=8，f是ab边上的中点，点d，e分别在ac，bc边上运动，且保持ad=ce连接de，df，ef在此运动变化的过程中，下列结论：dfe是等腰直角三角形；四边形cdfe不可能为正方形，de长度的最小值为4；四边形cdfe的面积保持不变；cde面积的最大值为8其中正确的结论是（）abcd显示解析二、填空题（每小题4分，共24分）13用反证法证明命题“三角形中必有一个内角小于或等于60”时，首先应假设这个三角形中显示解析14若（a-1）2+|b-2|=0，则以a、b为边长的等腰三角形的周长为显示解析15如图，在rtabc中，abc=90，

5、de是ac的垂直平分线，交ac于点d，交bc于点e，bae=20，则c=显示解析16如图，在abc中，bi、ci分别平分abc、acf，de过点i，且debcbd=8cm，ce=5cm，则de等于显示解析17如图，圆柱形容器中，高为1.2m，底面周长为1m，在容器内壁离容器底部0.3m的点b处有一蚊子，此时一只壁虎正好在容器外壁，离容器上沿0.3m与蚊子相对的点a处，则壁虎捕捉蚊子的最短距离为m（容器厚度忽略不计）显示解析18如图，在rtabc中，c=90，b=60，点d是bc边上的点，cd=1，将abc沿直线ad翻折，使点c落在ab边上的点e处，若点p是直线ad上的动点，则peb的周长的最小

6、值是显示解析三、解答题（每小题7分，共14分）19如图，c是ab的中点，ad=be，cd=ce求证：a=b显示解析20如图，两条公路oa和ob相交于o点，在aob的内部有工厂c和d，现要修建一个货站p，使货站p到两条公路oa、ob的距离相等，且到两工厂c、d的距离相等，用尺规作出货站p的位置（要求：不写作法，保留作图痕迹，写出结论）显示解析四、解答题（每小题10分，共40分）21在四边形abcd中，abcd，d=90，dca=30，ca平分dcb，ad=4cm，求ab的长度？显示解析22如图，在abc中，c=90，ad平分cab，交cb于点d，过点d作deab于点e（1）求证：acdaed；（

7、2）若b=30，cd=1，求bd的长显示解析23如图，把一个直角三角形acb（acb=90）绕着顶点b顺时针旋转60，使得点c旋转到ab边上的一点d，点a旋转到点e的位置f，g分别是bd，be上的点，bf=bg，延长cf与dg交于点h（1）求证：cf=dg；（2）求出fhg的度数显示解析24已知：如图，abc中，abc=45，dh垂直平分bc交ab于点d，be平分abc，且beac于e，与cd相交于点f（1）求证：bf=ac；（2）求证：ce12bf显示解析五、解答题（每小题12分.共24分）25如图，在abc中，d是bc是中点，过点d的直线gf交ac于点f，交ac的平行线bg于点g，dedf

8、交ab于点e，连接eg、ef（1）求证：bg=cf；（2）求证：eg=ef；（3）请你判断be+cf与ef的大小关系，并证明你的结论显示解析26abc中，ab=ac，点d为射线bc上一个动点（不与b、c重合），以ad为一边向ad的左侧作ade，使ad=ae，dae=bac，过点e作bc的平行线，交直线ab于点f，连接be（1）如图1，若bac=dae=60，则bef是三角形；（2）若bac=dae60如图2，当点d在线段bc上移动，判断bef的形状并证明；当点d在线段bc的延长线上移动，bef是什么三角形？请直接写出结论并画出相应的图形ka1dkagtgkqcwa3p tgz7r4i30ka1

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