Question

prove that a cyclic parallelogram is a rectangle.​

Answer 1

Answer:

Therefore, ∠1=∠2=∠3=∠4=900 which means all the interior angles of the given cyclic parallelogram are 900. Also we know that all the interior angles of a rectangle are equal to 900. Hence, a cyclic parallelogram is a rectangle.

Answer 2

Answer:

Ex 10.5, 12

Prove that a cyclic parallelogram is a rectangle.

Given: Let ABCD be a cyclic parallelogram

To prove: ABCD is a rectangle

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90°

Proof: A rectangle is a parallelogram with one angle 90° So, we have to prove angle 90°

Since ABCD is a parallelogram

ZA = ZC

(Opposite angles of parallelogram are equal)

In cyclic parallelogram ABCD

ZA + ZC = 180°

ZA + ZA = 180°

2ZA = 180°

ZA = 180° = 90°

(Sum of opposite angles of a cyclic quadrilateral is 180°)

(From (1))

So, ABCD is a parallelogram with one angle 90° Hence, ABCD is a rectangle