Q. 43.7( 11 Votes )

P, Q, R and S are

Answer :


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


In ΔADC, by mid-point theorem,


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


Now, in quad EOFR,


OE||FR, OF||ER


EOF = ERF = 90


Hence, PQRS is a rectangle.


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