如图,在平行四边形ABCD中,E为BC边上一点,且AB=AE. (1)求证:△ABC≌△EAD; (2)若AE平分∠DAB,∠EAC=25°,求∠AED的度数.

问题描述:

如图,在平行四边形ABCD中,E为BC边上一点,且AB=AE.

(1)求证:△ABC≌△EAD;
(2)若AE平分∠DAB,∠EAC=25°,求∠AED的度数.

(1)证明:∵四边形ABCD为平行四边形,∴AD∥BC,AD=BC.∴∠DAE=∠AEB.∵AB=AE,∴∠AEB=∠B.∴∠B=∠DAE.∵在△ABC和△AED中,AB=AE∠B=∠DAEAD=BC,∴△ABC≌△EAD.(2)∵AE平分∠DAB(已知),∴∠DAE=...