已知:如图在△ABC中,∠ACB=90°,D是AC的中点,DF∥BC,点E在BC的延长线上,且DE=AF.求证: (1)△ADF≌△DCE; (2)△ADF≌△CDF.

问题描述:

已知:如图在△ABC中,∠ACB=90°,D是AC的中点,DF∥BC,点E在BC的延长线上,且DE=AF.求证:

(1)△ADF≌△DCE;
(2)△ADF≌△CDF.

证明:(1)∵D是AC的中点,∴AD=CD,∵DF∥BC且∠ACB=90°,∴∠ADF=∠DCE=90°,在Rt△ADF和Rt△DCE中AD=CDAF=DE∴△ADF≌△DCE;(2)∵D是AC的中点,∴AD=CD,∵DF∥BC且∠ACB=90°,∴∠ADF=∠DCF=90°,在Rt...