Question

如图,在△ABC中,AD是角平分线,DE‖AC交AB于E,EF//AD,交BC于F,试问：EF是△BDE的角平分线

Answer 1

因为DE平行AC
说以∠BED=∠BAC
因为EF‖AD
所以∠BEF=∠BAD
又AD是角平分线
所以∠BAD=∠DAC
所以∠FED=∠DAC
所以∠BEF=∠FED
所以EF是△BDE的角平分线

Answer 2

AD是角平分线
∠CAD = ∠BAD
DE//AC
∠EDA = ∠CAD
EF//AD
∠DEF = ∠EDA = ∠CAD
∠BEF = ∠BAD = ∠CAD
即 ∠DEF = ∠BEF
所以 EF是△BDE的角平分线