△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
问题描述:
△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
答
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