In the given figure, PQRS is a parallelogram in which A and B are points on PQ and RS such that AP = AQ = SB = BR = 5 cm. The length of PC is 3 cm. What is the length of the diagonal PR?

In the quadrilateral AQBS, 

AQ = BS = 5 cm and AQ || BS.

∴ AQBS is a parallelogram.

⇒ AS || BQ

Converse of mid-point theorem states that the line drawn through the mid-point of one side of a triangle, which is parallel to another side, bisects the third side of the triangle.

In ΔPDQ, 

A is the mid-point of PQ and AC is parallel to DQ.

∴ PC = CD

Hence, CD = 3 cm

In ΔSRC, 

B is the mid-point of SR and SC is parallel to BD.

∴ CD = DR

⇒ DR = 3 cm

∴ PR = PC + CD + DR = (3 + 3 + 3) cm = 9 cm

Thus, the length of PR is 9 cm.