# Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC).

**Solution:**

Let's draw the given trapezium ABCD

Now, it can be observed that ΔDAC and ΔDBC lie on the same base DC and between the same parallels AB and CD.

According to Theorem 9.2: Two triangles on the same base (or equal bases) and between the same parallels are equal in area.

Area (ΔDAC) = Area (ΔDBC)

Now, Subtracting Area (ΔDOC) from both sides

Area (ΔDAC) - Area (ΔDOC) = Area (ΔDBC) - Area (ΔDOC)

Area (ΔAOD) = Area (ΔBOC) proved.

**Video Solution:**

## Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC).

### Maths NCERT Solutions Class 9 - Chapter 9 Exercise 9.3 Question 10:

**Summary:**

If diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O, then ar (AOD) = ar (BOC).