Question

Prove that if the diagonals of a parallelogram are equal then it is a rectangle.​

Answer 1

Answer:

here is the proof

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

Answer 2

${\bold{\underline{\boxed{Answer:}}}}$

Let ABCD be a parallelogram. To show that ABCD is a rectangle, we have to prove that one of its interior angles is 90º.

In ΔABC and ΔDCB,

⇒ AB = DC (Opposite sides of a parallelogram are equal)

⇒ BC = BC (Common)

⇒ AC = DB (Given)

∴ ΔABC ≅ ΔDCB (By SSS Congruence rule)

⇒ ∠ABC = ∠DCB

It is known that the sum of the measures of angles on the same side of transversal is 180º.

⇒ ∠ABC + ∠DCB = 180º (AB || CD)

⇒ ∠ABC + ∠ABC = 180º

⇒ 2∠ABC = 180º

⇒ ∠ABC = 90º

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