练习:△ABC中,BD平分∠ABC,AD⊥BD于D求证:∠C=∠BAD — ∠DAC
问题描述:
练习:△ABC中,BD平分∠ABC,AD⊥BD于D求证:∠C=∠BAD — ∠DAC
答
证明:延长AD,交BC于E.
∵∠ADB=∠EDB=90°;BD=BD;∠ABD=∠EBD.
∴⊿ABD≌⊿EBD(ASA),∠BED=∠BAD.
∴∠C=∠BED-∠DAC=∠BAD-∠DAC.