Question

如图,已知三角形ABC中,AB=AC,D是AB上一点,E是AC延长线上一点,且BD=CE,连接ED交BC于F,求证：DF

Answer 1

过D作DG∥AC交BC于G,则∠DGB=∠ACB,

∵AB=AC,∴∠B=∠ACB,∴∠DGB=∠B,

∴BD=DG,

∵BD=CE,∴DG=CE,

∵DG∥AC,∴∠FDG=∠E,∠FGD=∠FCE,

∴ΔFDG≌ΔFEC,

∴DF=EF.