**If the non-parallel sides of a trapezium are equal, prove that it is cyclic.**

**Solution:**

It is given that ABCD is a trapezium with and

We need to prove that ABCD is a cyclic quadrilateral.

**Construction: **Draw and .

In and , we have

** (Given)**

**(Each equal to )**

**(Distance between two parallel lines is constant.)**

Therefore, **by RHS congruence rule**, we have

**(Corresponding parts of congruent triangles are equal) (1)**

We also have **(Co-interior angles, ) (2)**

From **(1)** and **(2)**, we can say that

ABCD is a cyclic quadrilateral.

**(If the sum of a pair of opposite angles of a quadrilateral is , the quadrilateral is cyclic.)**