Prove that the midpoints of the sides of any convex quadrilateral are the vertices of a parallelogram.

(N/A) Let $ABCD$ be a convex quadrilateral. Let $P, Q, R,$ and $S$ be the midpoints of sides $AB, BC, CD,$ and $DA$ respectively.
Join $AC$. In $\triangle ABC$,$P$ and $Q$ are the midpoints of $AB$ and $BC$. By the Midpoint Theorem,$PQ \parallel AC$ and $PQ = \frac{1}{2} AC$ (Equation $1$).
In $\triangle ADC$,$S$ and $R$ are the midpoints of $AD$ and $CD$. By the Midpoint Theorem,$SR \parallel AC$ and $SR = \frac{1}{2} AC$ (Equation $2$).
From Equation $1$ and Equation $2$,we get $PQ \parallel SR$ and $PQ = SR$.
Since one pair of opposite sides of quadrilateral $PQRS$ is parallel and equal,$PQRS$ is a parallelogram.