北師大版八年級下冊《第1章三角形的證明》單元檢測卷

1、三角形的證明2014年單元檢測卷a（一）一、選擇題1等腰三角形的一個(gè)角是80，則它頂角的度數(shù)是（）a80b80或20c80或50d202下列命題的逆命題是真命題的是（）a如果a0，b0，則a+b0b直角都相等c兩直線平行，同位角相等d若a=6，則|a|=|b|3abc中，a：b：c=1：2：3，最小邊bc=4 cm，最長邊ab的長是（）a5cmb6cmc7cmd8cm4如圖，已知ae=cf，afd=ceb，那么添加下列一個(gè)條件后，仍無法判定adfcbe的是（）aa=cbad=cbcbe=dfdadbc5如圖，在abc中，b=30，bc的垂直平分線交ab于e，垂足為d若ed=5，則ce的長為（）

2、a10b8c5d2.56如圖，d為abc內(nèi)一點(diǎn)，cd平分acb，becd，垂足為d，交ac于點(diǎn)e，a=abe若ac=5，bc=3，則bd的長為（）a2.5b1.5c2d17如圖，ab=ac，beac于點(diǎn)e，cfab于點(diǎn)f，be、cf相交于點(diǎn)d，則abeacf；bdfcde；點(diǎn)d在bac的平分線上以上結(jié)論正確的是（）abcd8如圖所示，abbc，dcbc，e是bc上一點(diǎn)，bae=dec=60，ab=3，ce=4，則ad等于（）a10b12c24d489如圖所示，在abc中，ab=ac，d、e是abc內(nèi)兩點(diǎn)，ad平分bacebc=e=60，若be=6，de=2，則bc的長度是（）a6b8c9d10

3、10如圖，在abc中，c=90，b=30，以a為圓心，任意長為半徑畫弧分別交ab、ac于點(diǎn)m和n，再分別以m、n為圓心，大于mn的長為半徑畫弧，兩弧交于點(diǎn)p，連結(jié)ap并延長交bc于點(diǎn)d，則下列說法中正確的個(gè)數(shù)是（）ad是bac的平分線；adc=60；點(diǎn)d在ab的中垂線上；sdac：sabc=1：3a1b2c3d412如圖，在平面直角坐標(biāo)系xoy中，a（0，2），b（0，6），動點(diǎn)c在直線y=x上若以a、b、c三點(diǎn)為頂點(diǎn)的三角形是等腰三角形，則點(diǎn)c的個(gè)數(shù)是（）a2b3c4d513如圖，在等腰rtabc中，c=90，ac=8，f是ab邊上的中點(diǎn)，點(diǎn)d，e分別在ac，bc邊上運(yùn)動，且保持ad=ce連

4、接de，df，ef在此運(yùn)動變化的過程中，下列結(jié)論：dfe是等腰直角三角形；四邊形cdfe不可能為正方形，de長度的最小值為4；四邊形cdfe的面積保持不變；cde面積的最大值為8其中正確的結(jié)論是（）abcd二、填空題14用反證法證明命題“三角形中必有一個(gè)內(nèi)角小于或等于60”時(shí)，首先應(yīng)假設(shè)這個(gè)三角形中_15若（a1）2+|b2|=0，則以a、b為邊長的等腰三角形的周長為_16如圖，在rtabc中，abc=90，de是ac的垂直平分線，交ac于點(diǎn)d，交bc于點(diǎn)e，bae=20，則c=_17如圖，在abc中，bi、ci分別平分abc、acf，de過點(diǎn)i，且debcbd=8cm，ce=5cm，則de等

5、于_18如圖，圓柱形容器中，高為1.2m，底面周長為1m，在容器內(nèi)壁離容器底部0.3m的點(diǎn)b處有一蚊子，此時(shí)一只壁虎正好在容器外壁，離容器上沿0.3m與蚊子相對的點(diǎn)a處，則壁虎捕捉蚊子的最短距離為_m（容器厚度忽略不計(jì)）19如圖，在rtabc中，c=90，b=60，點(diǎn)d是bc邊上的點(diǎn)，cd=1，將abc沿直線ad翻折，使點(diǎn)c落在ab邊上的點(diǎn)e處，若點(diǎn)p是直線ad上的動點(diǎn)，則peb的周長的最小值是_3、 解答題20如圖，c是ab的中點(diǎn)，ad=be，cd=ce求證：a=b21如圖，兩條公路oa和ob相交于o點(diǎn)，在aob的內(nèi)部有工廠c和d，現(xiàn)要修建一個(gè)貨站p，使貨站p到兩條公路oa、ob的距離相等，

6、且到兩工廠c、d的距離相等，用尺規(guī)作出貨站p的位置（要求：不寫作法，保留作圖痕跡，寫出結(jié)論）22在四邊形abcd中，abcd，d=90，dca=30，ca平分dcb，ad=4cm，求ab的長度？23如圖，在abc中，c=90，ad平分cab，交cb于點(diǎn)d，過點(diǎn)d作deab于點(diǎn)e（1）求證：acdaed；（2）若b=30，cd=1，求bd的長24如圖，把一個(gè)直角三角形acb（acb=90）繞著頂點(diǎn)b順時(shí)針旋轉(zhuǎn)60，使得點(diǎn)c旋轉(zhuǎn)到ab邊上的一點(diǎn)d，點(diǎn)a旋轉(zhuǎn)到點(diǎn)e的位置f，g分別是bd，be上的點(diǎn)，bf=bg，延長cf與dg交于點(diǎn)h（1）求證：cf=dg；（2）求出fhg的度數(shù)25已知：如圖，abc

7、中，abc=45，dh垂直平分bc交ab于點(diǎn)d，be平分abc，且beac于e，與cd相交于點(diǎn)f（1）求證：bf=ac；（2）求證：第1章 三角形的證明2014年單元檢測卷a（一）答案一、bcdba ddabd 12.bb9.解：延長ed交bc于m，延長ad交bc于n，作dfbc，ab=ac，ad平分bac，anbc，bn=cn，ebc=e=60，bem為等邊三角形，efd為等邊三角形，be=6，de=2，dm=4，bem為等邊三角形，emb=60，anbc，dnm=90，ndm=30，nm=2，bn=4，bc=2bn=8，故選b13解：連接cf；abc是等腰直角三角形，fcb=a=45，cf

8、=af=fb；ad=ce，adfcef；ef=df，cfe=afd；afd+cfd=90，cfe+cfd=efd=90，edf是等腰直角三角形因此正確當(dāng)d、e分別為ac、bc中點(diǎn)時(shí)，四邊形cdfe是正方形因此錯(cuò)誤adfcef，scef=sadfs四邊形cefd=safc，因此正確由于def是等腰直角三角形，因此當(dāng)de最小時(shí)，df也最小；即當(dāng)dfac時(shí)，de最小，此時(shí)df=bc=4de=df=4；因此錯(cuò)誤當(dāng)cde面積最大時(shí)，由知，此時(shí)def的面積最小此時(shí)scde=s四邊形cefdsdef=safcsdef=168=8；因此正確故選b二、14每一個(gè)內(nèi)角都大于60 155 1635 173 18解：

9、如圖：高為1.2m，底面周長為1m，在容器內(nèi)壁離容器底部0.3m的點(diǎn)b處有一蚊子，此時(shí)一只壁虎正好在容器外壁，離容器上沿0.3m與蚊子相對的點(diǎn)a處，ad=0.5m，bd=1.2m，將容器側(cè)面展開，作a關(guān)于ef的對稱點(diǎn)a，連接ab，則ab即為最短距離，ab=1.3（m）故答案為：1.319解：連接ce，交ad于m，沿ad折疊c和e重合，acd=aed=90，ac=ae，cad=ead，ad垂直平分ce，即c和e關(guān)于ad對稱，cd=de=1，當(dāng)p和d重合時(shí)，pe+bp的值最小，即此時(shí)bpe的周長最小，最小值是be+pe+pb=be+cd+de=bc+be，dea=90，deb=90，b=60，de

10、=1，be=，bd=，即bc=1+，peb的周長的最小值是bc+be=1+=1+，故答案為：1+三、20證明：c是ab的中點(diǎn)，ac=bc，在acd和bce中，acdbce（sss），a=b21解：如圖所示：作cd的垂直平分線，aob的角平分線的交點(diǎn)p即為所求22解：d=90，dca=30，ad=4cm，ac=2ad=8cm，ca平分dcb，abcd，cab=acb=30，ab=bc，過b作beac，ae=ac=4cm，coseab=，cm23（1）證明：ad平分cab，deab，c=90，cd=ed，dea=c=90，在rtacd和rtaed中rtacdrtaed（hl）；（2）解：dc=de

11、=1，deab，deb=90，b=30，bd=2de=224（1）證明：在cbf和dbg中，cbfdbg（sas），cf=dg；（2）解：cbfdbg，bcf=bdg，又cfb=dfh，dhf=cbf=60，fhg=180dhf=18060=12025證明：（1）dh垂直平分bc，且abc=45，bd=dc，且bdc=90，a+abf=90，a+acd=90，abf=acd，bdfcda，bf=ac（2）由（1）得bf=ac，be平分abc，且beac，在abe和cbe中，abecbe（asa），ce=ae=ac=bfv2ohum32wgeauwydiawgmer4i30ka1dkaghn3x

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