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.

Rate this question :

E and F are respeNCERT Mathematics Exemplar

In a triangle, P,RD Sharma - Mathematics

In Fig. 14.99, ABRD Sharma - Mathematics

In Fig. 14.100, ARD Sharma - Mathematics

Prove that RS Aggarwal & V Aggarwal - Mathematics

Show that tRS Aggarwal & V Aggarwal - Mathematics

In the adjoRS Aggarwal & V Aggarwal - Mathematics

In the adjoRS Aggarwal & V Aggarwal - Mathematics

The parallel sideRS Aggarwal & V Aggarwal - Mathematics

In the given figuRS Aggarwal & V Aggarwal - Mathematics