证明：过点D作DP∥AC交BC于P，∴∠DPB=∠ACB，∠DPF=∠ECF．∵F是DE中点，∴DF=EF．在△DPF和△ECF中∠DPF＝∠ECF∠DFP＝∠EFCDF＝EF，∴△DPF≌△ECF（AAS），∴DP=EC．∵AB=AC，∴∠ABC=∠ACB，∴∠DPB=∠ABC，∴B...