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