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

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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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