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1、全等三角形练习,1.如图，AB、CD相交于点O，ACDB，OC=OD，E、F为AB上两点，且AE=BF，求证：CE=DF,证明：, ACDB, A=B,2,1,1=2,在AOC和BOD中,A=B,OC=OD,在AEC和BFD中,AOCBOD, AC=BD,AC=BD,A=B,AE=BF,AECBFD, CE=DF,2.如图，已知ABBC,DCBC,DEAC于M,AB=CE,求证:AC=DE,证明：,1,2,ABBC,DCBC,B=ECD=90,1+A=90,1+2=90, 2=A,在ABC和ECD中,A=2,AB=CE,B=ECD,ABCECD, AC=DE,DEAC,3.如图，已知M在AB上
2、,1=2，3=4.求证:AC=AD,证明：,在BCM和BDM中,1=2,3=4,BM=BM,BCMBDM, BC=BD,在ABC和ABD中,BC=BD,1=2,AB=AB,ABCABD, AC=AD,4.如图，已知AD、BC相交于O,OA=OC,OB=OD,EF过点O分别交AB、CD于E、F，且AOE=COF，求证：OE=OF,证明：,在AOB和COD中,AOB=COD,OA=OC,AOBCOD,在AOE和COF中,A=C,OB=OD, A=C,OA=OC,AOE=COF,AOECOF, OE=OF,5.如图，已知A=C,B=D,求证：AB=CD,证明：, BAD=BCD,B=D,1=2,在A
3、BC和ADC中,3=4,AC=AC,ABCADC, AB=CD,又 BAD+B+BCD+D=360, BAD+B=180,BAD+D=180, ABCD, ADBC, 1=2, 3=4,4,3,2,1,连结AC、BD,6.如图，已知AB=AC,AE=AF, 求证:(1)BD=CD,(2)AD平分BAC,1,2,4,3,证明：, AB=AC,AE=AF,1=2,(1)在ABF和ACE中,BE=CF, BE=CF, 1=2,AB=AC,BAF=CAE,AE=AF,ABFACE,在BED和CFD中, AB-AE=AC-AF,3=4,BEDCFD, BD=CD,6.如图，已知AB=AC,AE=AF,
4、求证:(1)BD=CD,(2)AD平分BAC,证明：,(2)在ABD和ACD中, BAD=CAD,AB=AC,BD=CD,ABDACD,1,2,4,3,AD=AD, AD平分BAC,7.如图A=B,AD=BC求证:ADC=BCD,证明：,在ABD和BAC中, AC=BD,DAB=CBA,AB=AB,ABDBAC,AD=BC, ADC=BCD,连结AC、BD,在ACD和BDC中,CD=CD,AC=BD,AD=BC,ACDBDC,8.如图，已知在ABC中,BAC=90,AB=AC,直线 MN经过点A,BDMN,CEMN,垂足分别是D、E. 求证:BD=AE,1,2,3,证明：, BDMN,CEMN
5、, BDA=AEC=90,且2+3=90, 1+2=90, 1=3,在ADB和CEA中,BDA=AEC,AB=AC,1=3,又 BAC=90, BD=AE,ADBCEA,9.如图，已知AB=AC,BEAC,垂足为E,CFAB,垂足为F,求证：AD平分BAC,证明：, BEAC,CFAB, AEB=AFC=90,在AEB和AFC中,AEB=AFC,AB=AC,BAE=CAF,AEBAFC, AE=AF,在RtAFD和RtAED中,AE=AF,AD=AD,AFDAED, 1=2,1,2, AD平分BAC,10.如图，已知AB=AD,AC=AE,DAB=EAC,BE、CD交于P.求证：AP平分DPE,G,H,证明：,作AGCD,AHBE, AP平分DPE, DAC=EAB,在ADC和ABE中,DAB=EAC, DAB+BAC=EAC+BAC,AB=AD,DAC=EAB,AC=AE,CD=BE,ADCABE,ADCABE, SADC=SABE,AG=AH,
