Prove:

∫D and E are the midpoint of AB and AC respectively.

∴DE is the center line of △ABC.

∴DE//BC and de = (BC 1/2).

DF is an extension of ∴ df//bc.de.

∵EF=DE,∴DF=DE+EF=2DE=BC

That is, DF is parallel and equal to BC.

∴ Quadrilateral BCFD is a parallelogram