如图,已知AB=DC,AC=DB,求证: (1)∠ABC=∠DCB (2)∠ABD=∠DCA

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如图,已知AB=DC,AC=DB,求证:(1)∠ABC=∠DCB(2)∠ABD=∠DCA如图,已知AB=DC,AC=DB,求证:(1)∠ABC=∠DCB(2)∠ABD=∠DCA如图,已知AB=DC,A

如图,已知AB=DC,AC=DB,求证: (1)∠ABC=∠DCB (2)∠ABD=∠DCA
如图,已知AB=DC,AC=DB,求证: (1)∠ABC=∠DCB (2)∠ABD=∠DCA

如图,已知AB=DC,AC=DB,求证: (1)∠ABC=∠DCB (2)∠ABD=∠DCA
①∵AB=DC,AC=DB
BC为△ABC和△BCD的公共边
∴△ABC≌△BCD(AAA)
∴∠ABC=∠DCB
②∵△ABC≌△BCD
∴∠A=∠D
∠AEB=∠DEC
而AB=DC
∴△ABE≌△CDE(AAS)
∴∠ABD=∠DCA