Question

△ABC中,AB=AC,D在AB上,E在AC延长线上,且BD=CE,DE交BC于P,求证DP=EP

Answer 1

证明：

过E作AB的平行线交BC的延长线于F,

AB=AC,↔∠B=∠ACB,

∴∠F=∠B=∠ACB=∠ECF,

∴EC=EF=BD,

∵AB//EF,

∴DP/PE=BD/EF=EC/EF=1,

∴DP=PE