# Prove that a cyclic parallelogram is a rectangle.

**Solution:**

The sum of either pair of opposite angles of a cyclic quadrilateral is 180°. Using this fact, we can show each angle of a cyclic parallelogram as 90°, proving the statement it is a rectangle.

Let ABCD be the cyclic parallelogram.

We know that opposite angles of a parallelogram are equal.

∠A = ∠C and ∠B = ∠D ... (1)

We know that the sum of either pair of opposite angles of a cyclic quadrilateral is 180°.

∠A + ∠C = 180°

∠A + ∠A = 180° (From equation (1))

2∠A = 180°

∠A = 90°

We know that if one of the interior angles of a parallelogram is 90°, all the other angles will also be equal to 90°.

Since all the angles in the parallelogram are 90°, we can say that parallelogram ABCD is a rectangle.

**Video Solution:**

## Prove that a cyclic parallelogram is a rectangle.

### Maths NCERT Solutions Class 9 - Chapter 10 Exercise 10.5 Question 12:

**Summary:**

We know that if one of the interior angles of a parallelogram is 90°, all the other angles will also be equal to 90°. Since all the angles in the parallelogram are 90°, we can say that parallelogram ABCD is a rectangle. Hence a cyclic parallelogram is a rectangle.