Using vector analysis proof that a quadrilateral is in fact a paralelogram

Question

Let D be the midpoint of line segment AC.

Let E be simultaneously the midpoint of line segments CB and DF.

Please note that the rightmost point is labeled F.

Goal: Using vector analysis proof that quadrilateral [ABFD] is in fact a paralelogram.

any hints?

Answer 1

Vectorially,$$\vec{BF}=\vec{BE}+\vec{EF}=\vec{EC}+\vec{DE}=\vec{DC}=\vec{AD}.$$