Question

在三角形ABC中,AD平分角BAC,点E在AB上,EF垂直于AD于O并交AC于F.求证:角BED=角DFC

Answer 1

∵AD平分∠BAC

∴ ∠BAD=∠CAD

∵EF⊥AD

∴ ∠AOE =∠AOF =90°,∠DOE =∠DOF =90°

∵AO=AO

∴△AOE全等△AOF

∴OE=OF,∠AEO =∠AFO

∵OD=OD,∠DOE =∠DOF =90°

∴△DOE全等△DOF

∴∠DEO =∠DFO

∵∠AEO+∠DEO+∠BED=180°

∠AFO+∠DFO+∠CFD=180°

∴∠BED =∠CFD