Question

$\square ABCD$ is a quadrilateral $P,Q,R,S$ are the mid point of side $AB,BC,CD,AC$ respectively. Prove that $\square PQRS$ is a parallelogram.

Answer 1

Argument behind $PQ=SR$ and $PQ\parallel AC$:-

In triangle ABC, P, Q are the mid points of the sides AB, BC.

So it follows that $PQ=\frac{1}{2}AC$......(1) and $PQ\parallel AC$.

Similarly from triangle ACD it follows that $SR=\frac{1}{2}AC$......(2) and $SR\parallel AC$.

From (1) and (2) we've,

$PQ=SR$.