Q. 33.5( 13 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 = BD.


In ΔADC, by mid-point theorem,


SR||AC and SR = AC


In ΔABC, by mid-point theorem,


PQ||AC and PQ = AC


SR = PQ = AC


Similarly,


In ΔBCD, by mid-point theorem,


RQ||BD and RQ = BD


In ΔBAD, by mid-point theorem,


SP||BD and SP = BD


SP = RQ = BD = AC


So,


SR = PQ = SP = RQ


Hence, PQRS is a rhombus.


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