Math, asked by abhishekgarg1237, 8 months ago

if the diagonal of a parallelogram are equal then show that it is a rectangle​

Answers

Answered by jiya5342
1

Answer:

Yes if diagonals of a parallelogram are equal then it is a rectangle.

Step-by-step explanation:

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.

Answered by Loveleen68
0

Answer:

hope it helps ............

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