Question

ABCD is a kite having AB = AD and BC = CD. Prove that the figure formed by joining the mid-points of the sides, in order, is a rectangle.

Answer 1

Given: A kite ABCD having AB = AD and BC = CD P, Q, R, S are the midpoint of sides AB, BC, CD, and DA respectively PQ, QR, RS and spare joined 

To prove: PQRS is a rectangle

Proof: 

Thus, in quadrilateral PQRS, a pair of opposite sides are equal and parallel. So PQRS is a parallelogram. Now, we shall prove that one angle of parallelogram PQRS it is a right angle 

Since AB = AD

Now, transversal PS cuts parallel lines SR and PQ at S and P respectively.