1、12如图,ABCDEC,A:ABC:BCA=3:5:10,(1)求D的度数;(2)求EBC的度数13如图,ABNACM,B和C是对应角,AB与AC是对应边,写出其他对应边和对应角14如图,已知ABDACE求证:BE=CD15如图,ABCDEF,BF=3,EF=2求FC的长16如图,ABCBDE,M、M分别为AB、DB中点,直线MM交CE于K试探索CK与EK的数量关系17如图,在ABC中,BE,CF分别是AC,AB边上的高线,BE,CF相交于O,连接AO交BC于D,且BCFCBE,ABC=70,求1和2的度数18如图,已知ABCADE,BC的边长线交AD于F,交AE于G,ACB=105,CAD=
2、10,ADE=25,求DFB和AGB的度数19如图,ABCDEC,1与2相等吗?请说明理由20如图,ABCEBD求证:1=221如图,ABCADE,CAD=10度,B=D=25度,EAB=120度,试求ACB的度数22如图,ABCDEF,ABC的周长是40cm,AB=10cm,BC=16cm,求DEF中,边DF的长度23如图:ABFDCE,写出相等的线段24如图,ABCADE中,BAAE,BAC=30,AD=5,求BD的长25如右图所示,已知ABDACE,试说明BE=CD26如图,ABCEFD,你能从图中找到几组平行线?请写出,并选择一组说明理由27如图,点B、E、C、F在一条直线上,BC=E
3、F ABDE,请你添加一个条件_,使ABCDEF并写出证明过程28如图,ACFDBE,E=F,若AD=11,BC=7,求线段AB的长29如图,已知ABCDEF,A=30,B=50,BF=2,求DFE的度数和EC的长30如图,ABCADE,B点的对应顶点是D点,若BAD=100,CAE=40,求BAC的度数参考答案1ABFDCEBAF=CDE,AFB=DEC,ABF=DCE,AB=DC,BF=CE,AF=DE;AFED,AC=BD,BFCE2ABCADE,DAE=BAC=(EABCAD)=DFB=FAB+B=FAC+CAB+B=10+55+25=90DGB=DFBD=9025=653证明:在AB
4、C和DCB中,AB=DC,AC=DB,BC=BC,ABCDCB(SSS),1=24AB=DE,AF=CD,A=D,则可得ABFDEC,BF=EC,又EF=BC,可得四边形BCEF是平行四边形,BFEC5ABCDEFAB=DE,BC=EF,AC=DFDE=2cm,EF=3cm,DF=4cm6ABCADE,B=D=40,E=C=30BAC=180BC=110;BAE=80,BAC=DAE=110BAD=DAEBAE=30DAC=BAC+BAD=110+30=1407.AOCBOD,A=B(全等三角形对应角相等)ACBD(内错角相等,两直线平行)8ABC中A=25BCA=180AB=18065ABC
5、DEF,BCA=DFE,BC=EF,EC=BF=3cmDFE=90,EC=3cm9(1)ABDEBD, ABD=EBD,BD是ABE的平分线;(2)DBEDCE,DEB=DEC,DEB+DEC=180DEB=DEC=90DEBC,DBEDCE,BE=EC10解:ABCDBC,A=110D=A=11011AECBFDAC=BD(全等三角形对应边相等)AC+CD=BD+CD,即AD=BC12(1)A+ABC+BCA=180,A:A=180=30,ABC=180=50,BCA=180=100又ABCDEC,D=A=30(2)ABCDEC,E=ABC=50BCA=100EBC=BCAE,5013ABN
6、ACM,B和C是对应角,AB与AC是对应边, 对应边:AN与AM,BN与CM; 对应角:BAN=CAM,ANB=AMC14ABDACE,AB=AC,AD=AE,ACAD=ABAE,即CD=BE15ABCDEFBC=EF=2 又FC=BFBC FC=32=116CK与EK的数量关系为相等,理由如下:延长MK到N,使得NK=MM,连接EM、CM、EN,如图, 可得NK+KM=MM+MK,即NM=MK,ABCBDE,M、M分别为AB、DB中点,EM=CM,BM=BM,EMD=CMB,由BM=BM得:BMM=BMM=KMD,NME=CMK,在EMN和CMK中,NM=MK,NME=CMK,EM=CM,E
7、MNCMK,(SAS)CK=EN,N=CKM=NKE,EK=EN,CK=EK17BCFCBE,FBC=ECB=70FBCECB=40,AB=AC,BE,CF分别是AC,AB边上的高线,BE,CF相交于O,ADBC,1=2=BAC=2018ABCADE,ACB=AED,ABC=ADE,CAB=EADADE=25ABC=ADE=25ACB=105CAB=180105DFB=DAB+ABC=50+10=85AGB=ACBGAC=10510=4519由题意:ABCDEC,BC=EC1=220ABCEBDA=E又AOD=BOE,A+AOD+1=E+BOE+2=18021ABCADE,CAB=EADEAB
8、=120EAB=EAD+CAD+CAB=2CAB+10=120CAB=55B=D=25ACB=180CABB=18055,即ACB的度数是10022已知,ABC的周长是40cm,AB=10cm,BC=16cm,AC=ABC的周长ABBC=401016=14(cm),DF=AC=14cm,所以边DF的长度为14cm23ABFDCE,AB=DC,BF=CE,AF=DE,DEC=AFE,OE=OF,AFFO=DEOE,AO=DO,BF=CE,BFFE=CEEF,EB=FC24由题意得:BAC=DAE=30,AB=AD,BAE=90CAD=30ABD=60ABD是等边三角形故可得:BD=AD=525A
9、BDACE,AD=AE,AC=AB,AEAB=ADAC,即BE=CD26ABEF,ACEDABCEFD,B=F,ACB=EDF,ABEF,ACED27ACB=F或AB=DE或A=D以下证明添加条件为AB=DE时,ABCDEFABDE,B=DEF在ABC和DEF中ABCDEF28ACFDBE,AC=DB,ACBC=DBBC,即AB=CD,AD=11,BC=7,AB=(ADBC)=(117)=2即AB=229A=3030DFE=ACB=100,EF=BC,EFCF=BCCF,即EC=BF,BF=2,EC=230ABCADE,BAC=DAE,BACCAE=DAECAE,即BAE=DAC,BAD=100BAE=(BADCAE)=(10040)=30BAC=BAE+CAE=30+40=70
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