Given, the quadrilateral ABCD is a rhombus.So, sides AB, BC, CD and AD are equal.
Now, in ΔPQS, we have
D and C are the mid – points of PQ and PS.
So, DC=12QS [by mid –d point theorem] . . . . . (i)
Similarly, in ΔPSR BC=12PR [by mid – point theorem] . . . . . .(ii)
As BC = DC [since, ABCD is a rhombus]
∴12QS=12PR [from Eqs. (i) and (ii) ]
Hence, diagonals of PQRS are equal.