Prove:

Make CG//AB pass through point C at point G and DF.

∵CG//AB

∴∠AFE =∞∠CGE (parallel straight lines with equal internal dislocation angles)

AE = AF

∴∠AFE=∠AEF (equiangular)?

∴∠CGE=∠AEF

∠∠AEF =∠∠CEG (equal to vertex angle)

∴∠CGE=∠CEG

∴CE=CG (equilateral)

∵CG//AB

∴△CDG∽△BDF

∴CD:BD=CG:BF

∴CD/BD=CE/BF