Question

(i) 3y – 1 = 26 [opposite sides are of equal length in a parallelogram]

(ii) y – 7 = 20 [diagonals bisect each other in a parallelogram]

Answer 1

Step-by-step explanation:

If the diagonals of a parallelogram are equal in length, then is the parallelogram a rectangle?

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

Answer 2

Step-by-step explanation:

If the diagonals of a parallelogram are equal in length, then is the parallelogram a rectangle?

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