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1、全等三角形的性质与判定(SSS、SAS、ASA、AAS)练习题1.如图,在△ABC中,∠A=90°,D、E分别是AC、BC上的点,若△ADB≌△EDB≌△EDC,则∠C=2.如图,把△ABC绕点C顺时针旋转35°,得到△A′B′C,A′B′交AC于点D,若∠A′DC=90°,则∠A=1题图2题图3题图4题图3.如图,△AOB中,∠B=30°,将△AOB绕点O顺时针旋转52°,得到△A′OB′,边A′B′与边OB交于点C(A′不在OB上),则∠A′CO=4.如图,△ABC≌△ADE,BC的延长线过点E,∠ACB=∠AED=1
2、05°,∠CAD=10°,∠B=50°,则∠DEF=5.如图,Rt△ABC中,∠BAC=90°,AB=AC,分别过点B、C作过点A的垂线BC、CE,垂足分别为D、E,若BD=3,CE=2,求DE的长.6.如图,AD是△ABC的角平分线,DE⊥AB,DF⊥AC,垂足分别是E、F,连接EF,交AD于G,试判断AD与EF的关系,并证明你的结论。7.如图所示,在△ABC中,AD为∠BAC的角平分线,DE⊥AB于E,DF⊥AC于F,△ABC的面积是28cm2,AB=20cm,AC=8cm,求DE的长。8.如图,AD=BD,AD⊥BC
3、于D,BE⊥AC于E,AD与BE相交于点H,则BH与AC相等吗?为什么?9.已知:BD、CE是△ABC的高,点F在BD上,BF=AC,点G在CE的延长线上,CG=AB,求证:AG⊥AF1.如图:在△ABC中,BE、CF分别是AC、AB两边上的高,在BE上截取BD=AC,在CF的延长线上截取CG=AB,连结AD、AG.试判断AD与AG的关系如何?并证明之.2.已知,如图:AB=AE,∠B=∠E,∠BAC=∠EAD,∠CAF=∠DAF,求证:AF⊥CD12.已知:∠B=∠E,且AB=AE。求证:OD=OC13.已知:∠3=∠4
4、,AE⊥BC于点D.求证:∠1=∠214.已知:∠3=∠4,∠1=∠2,且T,U,S三点共线。求证:RS=SE15.已知:AD//BC,FC//AE,且FC=AE。求证:AB=CD16.已知:AE//DF且,AE=FD,求证:G是BC中点17.已知:AE//CF,AD//BC且DF=BE求证:AB=CD18.如图,AD=BC且AD//BC,G是BD的中点。求证:AE=FC19.已知:ED//BF,AB//CD,点G是BD的中点.求证:EM=FN20.如图,已知AB∥CD,O是∠ACD与∠BAC的平分线的交点,OE⊥AC于点
5、E,且OE=2,则AB与CD之间的距离是多少?21.如图,过线段AB的两个端点作射线AM、BN,使AM∥BN,∠MAB、∠NBA的平分线AE、BE交于点E.(1)求∠AEB是多少度?(2)过点E作一直线交AM于D,交BN于C,观察线段DE、CE,你有何发现?并证明.(3)无论DC的两端点在AM、BN如何移动,只要DC经过点E,①AD+BC=AB;②AD+BC=CD谁成立?并说明理由。Whenyouareoldandgreyandfullofsleep,Andnoddingbythefire,takedownthisbook
6、,Andslowlyread,anddreamofthesoftlookYoureyeshadonce,andoftheirshadowsdeep;Howmanylovedyourmomentsofgladgrace,Andlovedyourbeautywithlovefalseortrue,Butonemanlovedthepilgrimsoulinyou,Andlovedthesorrowsofyourchangingface;Andbendingdownbesidetheglowingbars,Murmur,alit
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8、eButwhenundoubtedlyknowingthelovefrombothYetcannotbetogether.ThefurthestdistanceintheworldIsnotbeingapartwhilebeinginloveButwhenIplainlycannotresistthey