Question

Prove that a cyclic parallelogram is a rectangle.

Answer 1

Given,

ABCD is a cyclic parallelogram.

To prove

ABCD is a rectangle.

Proof:

∠1 + ∠2 = 180° ...Opposite angles of a cyclic parallelogram

Also, Opposite angles of a cyclic parallelogram are equal.Thus,

∠1 = ∠2

⇒ ∠1 + ∠1 = 180°

⇒ ∠1 = 90°

One of the interior angle of the parallelogram is right angled.

Thus,

ABCD is a rectangle.

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hope this helped

Answer 2

Let ABCD be a cyclic parallelogram,

angle A + angle C = 180° ......(1)

(Opp. angles of a cyclic quadrilateral)

We know that opposite angles of a parallelogram are equal.

Therefore, angle A = angle C and angle B = angle D

From equation (1)

angle A + angle C = 180°

angle A + angle A = 180°

2angle A = 180°

angle A = 90°

Parallelogram ABCD has one of its interior angles as 90°. Therefore, it is a rectangle.