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1、北师大版八年级下册第1章 三角形的证明2014年同步练习卷A（6）一、选择题（共7小题，每小题3分，满分21分）1如果三角形的三个内角度数比为1：1：2，则这个三角形为（）A锐角三角形B钝角三角形C非等腰直角三角形D等腰直角三角形显示解析2下面命题不正确的是（）A两个内角分别是50和65的三角形是等腰三角形B两个外角相等的三角形是等腰三角形C一个外角的平分线平行于一边的三角形是等腰三角形D两个内角不相等的三角形不是等腰三角形显示解析3下列选项中，可以用来证明命题“若a21，则a1”是假命题的反例是（）Aa=-2Ba=-1Ca=1Da=2显示解析4反证法证明“三角形中至少有一个角不小于60”先应
2、假设这个三角形中（）A有一个内角小于60B每个内角都小于60C有一个内角大于60D每个内角都大于60显示解析5如图，在ABC中，AB=AC，E是AB的中点，以点E为圆心，EB为半径画弧，交BC于点D，连接ED并延长到点F，使DF=DE，连接FC，若B=70，则F的度数是（）A40B70C50D45显示解析6如图所示的正方形网格中，网格线的交点称为格点已知A、B是两格点，如果C也是图中的格点，且使得ABC为等腰三角形，则点C的个数是（）A6B7C8D9显示解析7如图，一艘海轮位于灯塔P的南偏东70方向的M处，它以每小时40海里的速度向正北方向航行，2小时后到达位于灯塔P的北偏东40的N处，则N处
3、与灯塔P的距离为（）A40海里B60海里C70海里D80海里显示解析二、填空题（共3小题，每小题3分，满分9分）8如图所示，在ABC中，AB=AC，点D、E在BC边上，ABD=DAE=EAC=36，则图中共有等腰三角形的个数是显示解析9如图，在ABC中，B与C的平分线交于点O，过点O作DEBC，分别交AB、AC于点D、E若AB=5，AC=4，则ADE的周长是显示解析10如图，AD是ABC的边BC上的高，由下列条件中的某一个就能推出ABC是等腰三角形的是BAD=ACD；BAD=CAD；AB+BD=AC+CD；AB-BD=AC-CD显示解析三、解答题（共3小题，满分0分）11证明题：如图所示，在A
4、BC中，AB=AC，APBAPC，求证：PBPC显示解析12如图，在ABC中，AB=AC，AD是高，AM是ABC外角CAE的平分线（1）用尺规作图方法，作ADC的平分线DN；（保留作图痕迹，不写作法和证明）（2）设DN与AM交于点F，判断ADF的形状（只写结果）显示解析13已知AOB及其内部一点P，试讨论以下问题的解答：（1）如图，若点P在AOB的平分线上，我们可以过P点作直线垂直于角平分线，分别交OA、OB于点C、D，则可以得到OCD是以CD为底边的等腰三角形；若点P不在AOB的平分线上（如图），你能过P点作直线，分别交OA、OB于点C、D，得到OCD是等腰三角形，且CD是底边吗？请你在图中
5、画出图形，并简要说明画法（2）若点P不在AOB的平分线上（如图），我们可以过P点作PQOA，并作QPR=AOB，直线PR分别交OA、OB于点C、D，则可以得到OCD是以OC为底的等腰三角形请你说明这样作的理由（3）若点P不在AOB的平分线上，请你利用在（2）中学到的方法，在图中过P点作直线分别交OA、OB于点C、D，使得OCD是等腰三角形，且OD是底边保留画图的痕迹，不用写出画法QcWA3PtGZ7R4I30kA1DkaGhn3XtKknBYCUDxqA7FHYi2CHhI92tgKQcWA3PtGshLs50cLmTWN60eo8Wgqv7XAv2OHUm32WGeaUwYDIAWGMeR4
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