Question

If the diagonals of a parallelogram are equal, then show that it is a rectangle.​

Answer 1

Answer:

Let ABCD be a parallelogram.

To show that ABCD is a rectangle, we have to prove that one of

its interior angles is 90°

In ΔABC and ΔDCB,

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

BC = BC (Common)

AC = DB (Given)

By SSS congruence rule,

ΔABC ≅ ΔDCB

So, ∠ABC = ∠DCB

It is known that the sum of measures of angles on the same side of traversal is 180°

∠ABC + ∠DCB = 180° [AB||CD]

=> ∠ABC + ∠ABC = 180°

=> 2∠ABC = 180°

=> ∠ABC = 90°

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

#Hope it helps u ✌✌