Question

if the diagonals of a parallelogram are equal then show that it's a rectangle......my answer is correct or wrong??​

Answer 1

Answer:

Given,

AC = BD

To show,

To show ABCD is a rectangle we have to prove

that one of its interior angle is right angled.

Proof,

In ΔABC and ΔBAD,

BC = BA (Common)

AC = AD (Opposite sides of a parallelogram are equal)

AC = BD (Given)

Therefore, ΔABC ≅ ΔBAD by SSS congruence condition.

∠A = ∠B (by CPCT)

also,

∠A + ∠B = 180° (Sum of the angles on the same side of the transversal)

⇒ 2∠A = 180°

⇒ ∠A = 90° = ∠B

Thus ABCD is a rectangle.