# The line segments

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

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