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