If two opposite sides of a cyclic quadrilateral are equal, then prove that the other two sides are parallel.

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Solution

Sol:
Given: Cyclic quadrilateral ABCD such that AD = BC
To Prove: AB parallel to CD
Construction: Join BD
Proof: Given that AD = BC
Arc DA = Arc BC
∠2 = ∠1 [Equal chords subtend equal angles at the circumference of the circle]
The angles ∠1and ∠2 are alternate interior angles.
Therefore, AB is parallel to CD.

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Similar questions

If two sides of a cyclic-quadrilateral are parallel; prove that :

(i) its other two sides are equal.

(ii) its diagonals are equal.

If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that is diagonals are equal.

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