Question

prove that a cyclic parallelogram is a rectangle​

Answer 1

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.

angle a = angle c and angle b = angle d

From equation (1),

angle a + angle c  = 180

2 angle a = 180

angle a = 90

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

Answer 2

Answer:

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°