1全等三角形的判定班级:姓名:1.已知AD是⊿ABC的中线,BE⊥AD,CF⊥AD,求证BE=CF。2.已知AC=BD,AE=CF,BE=DF,求证AE∥CF3.已知AB=CD,BE=DF,AE=CF,求证AB∥CD4.已知在四边形ABCD中,AB=CD,AD=CB,求证AB∥CD5.已知∠BAC=∠DAE,∠1=∠2,BD=CE,求证⊿ABD≌⊿ACE.6.已知CD∥AB,DF∥EB,DF=EB,求证AF=CE7.已知BE=CF,AB=CD,∠B=∠C,求证AF=DE8.已知AD=CB,∠A=∠C,AE=CF,求证EB∥DF9.已知M是AB的中点,∠1=∠2,MC=MD,求证∠C=∠D。10.已知,AE=DF,BF=CE,AE∥DF,求证AB=CD。11.已知∠1=∠2,∠3=∠4,求证AC=AD12.已知∠E=∠F,∠1=∠2,AB=CD,求证AE=DF13.已知ED⊥AB,EF⊥BC,BD=EF,求证BM=ME。14.在⊿ABC中,高AD与BE相交于点H,且AD=BD,求证⊿BHD≌⊿ACD。ACDB1234ABCDEF12ABCEHDACMEFBDABCDFEACBDEFDCFEABABCDADEBC12ADCEFBACDBEFBADFECMABCD12DCFEAB215.已知∠A=∠D,AC∥FD,AC=FD,求证AB∥DE。16.已知AC=AB,AE=AD,∠1=∠2,求证∠3=∠4。17.已知EF∥BC,AF=CD,AB⊥BC,DE⊥EF,求证⊿ABC≌⊿DEF。18.已知AD=AE,∠B=∠C,求证AC=AB。19.已知AD⊥BC,BD=CD,求证AB=AC20.已知∠1=∠2,BC=AD,求证⊿ABC≌⊿BAD。21.已知AB=AC,∠1=∠2,AD=AE,求证⊿ABD≌⊿ACE.22.已知BE∥DF,AD∥BC,AE=CF,求证⊿AFD≌⊿CEB23.已知AD=AE,BD=CE,∠1=∠2,求证⊿ABD≌⊿ACE24.已知AB=AC,AD=AE,∠1=∠2,求证CE=BD。25.已知CE⊥AB,DF⊥AB,AC∥DB,AC=BD,求证CE=DF26.如图,AD=BC,AE=BE,求证∠C=∠D。ABCEFDCAEBFDABCEDFADEBCABCDABCDO12BADFECABCDE12ACDBEFG12ADEBC1234ACDEBADBEC12327.已知∠1=∠2,AC=BD,E,F,A,B在同一直线上,求证∠3=∠428.已知DO⊥BC,OC=OA,OB=OD,求证CD=AB29.已知CE=DF,AE=BF,AE⊥AD,FD⊥AD,求证⊿EAB≌⊿FDC30.已知AB与CD相交于点E,EA=EC,ED=EB,求证⊿AED≌⊿CEB31.已知AB=AC,D,E分别是AB,AC的中点。求证BE=CD。32.已知DE=FE,FC∥AB,求证AE=CE。33.已知CE⊥AB,DF⊥AB,CE=DF,AE=BF,求证⊿CEB≌⊿DFA。34.如图,D,E,F,B在一条直线上,AB=CD,∠B=∠D,BF=DE,求证(1)AE=CF(2)AE∥CF。35.已知,点C是AB的中点,CD∥BE,且CD=BE,求证∠D=∠E。36.已知,E、F是AB上的两点,AE=BF,又AC∥DB,AC=DB,求证CF=DE。AEDCBOCDAEFB2134BACDEFCDEFABDAECB12BADFECACBDECAEBFDADBEFCACBED437.已知,AC⊥CE,AC=CE,∠ABC=∠DEC=900,求证BD=AB+ED。38.⊿ABC≌⊿A′B′C′,AD与A′D′分别是中线,求证AD=A′D′。39.已知:如图,E,B,F,C四点在同一直线上,∠A=∠D=90°,BE=FC,AB=DF.求证:∠E=∠C40.已知:如图,DN=EM,且于于E,BM=CN.求证:∠B=∠C.41.已知:如图,AE,FC都垂直于BD,垂足为E、F,AD=BC,BE=DF.求证:OA=OC.42.已知:如图,AB=CD,D、B到AC的距离DE=BF.求证:AB∥CD.43.已知:如图于于C,求证:EA=EB.44.如图,已知:∠ACB和∠ADB都是直角,BC=BD,E是AB上任一点,求证:CE=DE.45.已知:如图,∠A=∠D=90°,AC,BD交于O,AC=BD,求证:OB=OC.ABCDEABCDA′B′C′D′