The line segments joining the midpoints of the adjacent sides of a quadrilateral form

In the given quadrilateral ABCD

P, Q, R, S are the midpoints of the sides AB, BC, CD and AD respectively.

Construction: - Join AC

In Δ ABC and Δ ADC

P and Q are midpoints of AB and CB

S and R are midpoints of AD and DC

So by Mid Point Theorem

PQ ∥ AC and PQ = 1/2 AC………….1

And SR ∥ AC and SR = 1/2 AC………………2

From 1 and 2

PQ ∥ SR and PQ = SR

Since a pair of opposite side is equal (= ) and parallel (∥)

PQRS is a parallelogram