**Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a ****trapezium.**

**Solution:**

We have quadrilateral ABCD. Diagonals AC and BD intersect each other at O.

It is given that

**(1)**

We can see that and are on the same base CD. ** (2)**

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

**(Two triangles having the same base and equal areas lie between the same parallels.)**

ABCD is a trapezium.