Question

如图,AD是△ABC的角平分线,BE⊥AD,交AD的延长线于E,EF平行AC交AB于F.求证:AF=BF

Answer 1

∵AD平分∠BAC,

∴∠BAD=∠CAD,

∵EF∥AC,∴∠CAB=∠AEF,

∴∠BAD=∠AEF,

∴AF=EF,

∵AE⊥BE,

∴∠BAD+∠B=90°,∠BEF+∠AEF=90°,

∴∠B=∠BEF(等角的相等),

∴BE=EF,

∴AF=BF.