Question

3. Prove that parallelogram is a rectangle if its diagonals
are of equal length​

Answer 1

Answer:

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 to prove 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 = ∠SRQ

Since adjacent angles of a parallelogram are supplementary. (Consecutive interior angles)

∠PQR + ∠SRQ= 180º

⇒ ∠PQR + ∠PQR= 180º

⇒ 2∠PQR= 180º

⇒ ∠PQR = 90º

Since PQRS is a parallelogram and one of its interior angles is 90º, PQRS is a rectangle.