Question

P, Q, R and S are respectively the mid-points of sides AB, BC, CD and DA of
quadrilateral ABCD in which AC = BD and AC ⊥ BD. Prove that PQRS is a square. PLEASE GIVE LITTLE BIT SHORT ANS​

Answer 1

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

Also, AC ⊥ BD

To prove PQRS is a rectangle.

Proof Since, AC ⊥ BD .

∠COD = ∠AOD= ∠AOB= ∠COB = 90°