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If two opposite sides of a cyclic quadri...

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

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Given: In cyclic quadrilateral `ABCD`, `AD=BC`.
To Prove: `AB∥BC`
Construction: Join `BD`.
Proof: `AD=BC` [Given]
`Arc DA=Arc BC`
`∠1=∠2` [Equal chord subtend equal angle at the circumference of the circle]
But `∠1` and `∠2` are alternate interior angles.
`∴AB` is parallel to `CD`.
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