如图,在△ABE中,AB=AE,AD=AC,∠BAD=∠EAC,BC、DE交于点O. 求证:(1)△ABC≌△AED; (2)OB=OE.

问题描述:

如图,在△ABE中,AB=AE,AD=AC,∠BAD=∠EAC,BC、DE交于点O.
求证:(1)△ABC≌△AED;
(2)OB=OE.

证明:(1)∵∠BAD=∠EAC,∴∠BAD+∠DAC=∠EAC+∠DAC,即∠BAC=∠EAD.在△ABC和△AED中AB=AE∠BAC=∠EADAC=AD,∴△ABC≌△AED(SAS).(2)∵由(1)知△ABC≌△AED∴∠ABC=∠AED,∵AB=AE,∴∠ABE=∠AEB,∴...