Question

If the diagonals of a parallelogram are equal then prove that it is a rectangle​

Answer 1

Step-by-step explanation:

Yes if diagonals of a parallelogram are equal then it is a rectangle.Let PQRS be a parallelogram. To show that PQRS is a rectangle, we have toprove that one of its interior angles is 90º.In ΔPQR and ΔSRQ,PQ = SR (Opposite sides of a parallelogram are equal)QR = QR (Common)PR = SQ (Given)∴ ΔPQR ≅ ΔSRQ (By SSS Congruence rule)⇒ ∠PQR = ∠SRQSince adjacent angles of a parallelogram are supplementary. (Consecutive interior angles)∠PQR + ∠SRQ= 180º⇒ ∠PQR + ∠PQR= 180º⇒ 2∠PQR= 180º⇒ ∠PQR = 90ºSince PQRS is a parallelogram and one of its interior angles is 90º, PQRS is a rectangle.