Question

In ΔABC, D and E are the midpoints of the sides AB and BC respectively. F is any point on the side AC. Also, EF is parallel to AB. Prove that BFED is a parallelogram.

Remark: Figure is incorrect in Question

Answer 1

From the figure EF || AB and E is the midpoint of BC.
Therefore, F is the midpoint of AC.
Here EF || BD, EF = BD as D is the midpoint of AB.
BE || DF, BE = DF as E is the midpoint of BC.
Therefore BEFD is a parallelogram.
Remark: Figure modified.