如图,已知∠A=∠B.OA=OB,AD与BC相交于点E,请说明oE平分∠AOB的理由

∠AOB=∠AOB
OA=OB
∠A=∠B
△AOD≌△BOC
OD=OC
OB=OA
OB-OD=OC-OA
BD=AC
∠B=∠A
∠BED=∠AEC
△BED≌△AEC
AE=EB
OA=OB
OE=OE
△AOE≌△BOE
∠AOE=∠BOE
OE平分∠AOB