已知:如图,△ABC中,AD=DB,∠1=∠2. 求证: (1)∠AED=∠BAC; (2)△ABC∽△EAD.

问题描述:

已知:如图,△ABC中,AD=DB,∠1=∠2.
求证:
(1)∠AED=∠BAC;
(2)△ABC∽△EAD.

证明:(1)∵AD=DB,
∴∠B=∠BAD.
∵∠1=∠2,
∴∠AED=∠BAC.
(2)∵∠B=∠BAD,∠AED=∠BAC,
∴△ABC∽△EAD.