已知:如图,△ABC中,D,E分别在AB,AC上,且AD=AE,连结DE并延长,交BC延长线于F.求证:CF:BF=CE:BD.
问题描述:
已知:如图,△ABC中,D,E分别在AB,AC上,且AD=AE,连结DE并延长,交BC延长线于F.求证:CF:BF=CE:BD.
答
证明:过点C作CG∥AB交DF于G,
∵AD=AE,
∴∠ADE=∠AED,
∵CG∥AB,
∴∠ADE=∠EGC,
∵∠AED=∠CEG,
∴∠CEG=∠CGE,
∴CE=CG,
∵CG∥AB,
∴
=FC BF
,CG BD
∴CF:BF=CE:BD.