# P, Q, R and S are

Given, P, Q, R and S are mid-points of the sides AB, BC, CD and DA, respectively.

Also,

AC is perpendicular to BD

COD = AOD = AOB = COB = 90

SR||AC and SR = AC

In ΔABC, by mid-point theorem,

PQ||AC and PQ = AC

PQ||SR and SR = PQ = AC

Similarly,

SP||RQ and SP = RQ = BD

OE||FR, OF||ER

EOF = ERF = 90

Hence, PQRS is a rectangle.

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