Question

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

Answer 1

Given: In cyclic quadrilateral $ABCD$, $AD=BC$.

To Prove: $AB\parallel BC$

Construction: Join $BD$.

Proof:

$AD=BC$ ...Given

Arc $DA=$ Arc $BC$

$\angle 1=\angle 2$ ....[Equal chord subtend equal angle at the circumference of the circle]

But $\angle 1$and $\angle 2$ are alternate interior angles.

$\therefore AB$ is parallel to $CD$.