如图,已知AB=AE,BC=ED,AF⊥CD于F,CF=DF. (1)求证:AC=AD; (2)求证:∠B=∠E.

问题描述:

如图,已知AB=AE,BC=ED,AF⊥CD于F,CF=DF.

(1)求证:AC=AD;
(2)求证:∠B=∠E.

证明:(1)∵AF⊥CD于F,CF=DF,
∴△ACD为等腰三角形.
∴AC=AD.
(2)∵AC=AD,AB=AE,BC=ED,
∴△ABC≌△AED(SSS).
∴∠B=∠E.