全等三角形的性质与判定(SSS、SAS、ASA、AAS)练习题

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=105°，∠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于D，BE⊥AC于E，AD与BE相交于点H，则BH与AC相等吗？为什么？EFACBDBDECAGBCADEFBCADEFCAOBA'B'BACDEDB'BCAA'HBCADE9.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⊥AF10.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.11.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,AE⊥BC于点D.求证：∠1=∠2EBCAGDFHFBCAGEDOEDACB4321EBCADCDABEF14.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=CDFDCABEFCGADBEFDCABE1234ERSTU18.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,FGCABDENMFGCABDEBDACOEMNABEDCAndnoddingbythefire,takedownthisbook,Andslowlyread,anddreamofthesoftlookYoureyeshadonce,andoftheirshadowsdeep;Howmanylovedyourmomentsofgladgrace,Andlovedyourbeautywithlovefalseortrue,Butonemanlovedthepilgrimsoulinyou,Andlovedthesorrowsofyourchangingface;Andbendingdownbesidetheglowingbars,Murmur,alittlesadly,howlovefledAndpaceduponthemountainsoverheadAndhidhisfaceamidacrowdofstars.ThefurthestdistanceintheworldIsnotbetweenlifeanddeathButwhenIstandinfrontofyouYetyoudon'tknowthatIloveyou.ThefurthestdistanceintheworldIsnotwhenIstandinfrontofyouYetyoucan'tseemyloveButwhenundoubtedlyknowingthelovefrombothYetcannotbetogether.ThefurthestdistanceintheworldIsnotbeingapartwhilebeinginloveButwhenIplainlycannotresisttheyearningYetpretendingyouhaveneverbeeninmyheart.ThefurthestdistanceintheworldIsnotstrugglingagainstthetidesButusingone'sindifferentheartTodiganuncrossableriverFortheonewholovesyou.