Given: D and E are the midpoints of side AB and side AC respectively.
ED = DF
To prove: AFBE is a parallelogram.
Proof:
seg AB and seg EF are the diagonals of AFBE.
seg AD ≅ seg DB [Given]
seg DE ≅ seg DF [Given]
∴ Diagonals of AFBE bisect each other.
∴ AFBE is a parallelogram. [ By test of parallelogram]