已知:如图,AB=AC,AD=AE,∠BAC=∠DAE, 求证:BD=CE.

问题描述:

已知:如图,AB=AC,AD=AE,∠BAC=∠DAE,
求证:BD=CE.

证明:∵∠DAE=∠BAC,
∴∠DAE-∠BAE=∠EAC-∠BAE,
∴∠BAD=∠CAE,
在△BAD和△CAE中,

AD=AE
∠BAD=∠CAE
AB=AC

∴△BAD≌△CAE(SAS),
∴BD=EC.