如图,△ABC中,∠BAC=90°,AD⊥BC于D,BF平分∠ABC交AD于E.(1)∠AEF与∠AFE相等吗?请说明理由.(

问题描述:

如图,△ABC中,∠BAC=90°,AD⊥BC于D,BF平分∠ABC交AD于E.(1)∠AEF与∠AFE相等吗?请说明理由.(
(2)比较∠C与∠BED的大小关系,说明理由.

1、∠AEF=∠AFE证明:∵∠BAC=90∴∠C+∠ABC=90∵AD⊥BC∴∠ABC+∠BAD=90∴∠BAD=∠C∵BF平分∠ABC∴∠ABF=∠CBF∵∠AEF=∠ABF+∠BAD∴∠AEF=∠CBF+∠C∵∠AFE=∠CBF+∠C∴∠AEF=∠AFE AEF=∠AFE2、∠BED...