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

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/06 11:19:50
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

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