如图所示,在△ABC中,AB=AC,D是AB上任意一点,且BD=CE,连接DE交BC于F. 求证:FD=FE.
问题描述:
如图所示,在△ABC中,AB=AC,D是AB上任意一点,且BD=CE,连接DE交BC于F.
求证:FD=FE.
答
证明:如答图所示,
过D作DH∥AC交BC于H,则∠ACB=∠DHB,DH∥CE,
∵AB=AC,
∴∠B=∠ACB.
∴∠B=∠DHB.
∴DB=DH.
∵BD=CE,
∴DH=CE.
∵DH∥CE,
∴△HDF∽△CEF.
∴
=FD FE
=1.DH EC
即FD=FE.