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Question

Prove that the non-rectangular parallelogram is not a cyclic quadrilateral.


Solution

Consider the non-rectangular parallelogram, ABCD.

We know that opposite angles of a parallelogram are equal.

∴ ∠A = C … (1)

Let us suppose that ABCD is a cyclic quadrilateral.

We know that opposite angles of a cyclic quadrilateral are supplementary.

⇒ ∠A + C = 180° 

⇒ ∠A + A = 180° (From equation (1))

2A = 180°

⇒ ∠C = 90°

This is a contradiction to the given condition that ABCD is a non-rectangular parallelogram.

Thus, our supposition was wrong.

Hence, a non- rectangular parallelogram is not a cyclic quadrilateral.


Mathematics
Mathematics Part I
Standard X

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