Question

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

Answer 1

Given-

Let ABCD is the required parallelogram.

Given, AC = BD       {Diagonals}

To prove-

ABCD is a  rectangle.

Proof-

Since rectangle is a parallelogram with one angle = 90°,

we can prove that one of its interior angles is  90°.

In ΔABD and ΔACD,

1. AB = DC  (opposite sides)
2. DA = DA  (common)
3. BD = AC  (diagonals)

∴ ΔABD ≅ ΔACD

⇒ ∠BAD = ∠CDA

Now,

AB ║ DC

and AC is the transversal.

∴ ∠A + ∠D = 180°  (adjacent angles)

or, ∠A + ∠A = 180°   (∠A = ∠D)

or, 2∠A = 180°

or, ∠A = (180/2)°

or, ∠A = 90°

Hence, one angle of the parallelogram is 90°.

So, ABCD is a rsectangle.   {Proved}

Answer 2

Step-by-step explanation:

hope it helps.......☺️