△ABC中,AB=AC,AD=2,AD是△ABC的中线,AE是∠BAD的角平分线,DF∥AB交AE的延长线于点F,求DF的长.

问题描述:

△ABC中,AB=AC,AD=2,AD是△ABC的中线,AE是∠BAD的角平分线,DF∥AB交AE的延长线于点F,求DF的长.

∵AE平分∠BAD
∴∠BAE=∠DAE
∵DF∥AB
∴∠DFA=∠BAE
∴∠DFA=∠DAE
∴DF=AD
∵AD=2
∴DF=2