**P, Q, R and S are respectively the mid-points of sides AB, BC, CD and DA of quadrilateral ABCD in … BD and AC ⊥ BD. Prove that PQRS…**

###### Answers:

Given In quadrilateral ABCD, P, Q, R and S are the mid-points of the sides AB, BC, CD and DA, respectively.

Also, AC = BD and AC ⊥ BD.

To prove PQRS is a square.

Proof Now, in ΔADC, S and R are the mid-points of the sides AD and DC respectively, then by mid-point theorem,