**ABCD is a trapezium with . A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).**

**[Hint : Join CX.]**

**Solution:**

We have trapezium ABCD with . It is also given that .

We need to prove that

We can note that and are on the same base AX and between the same parallels AB and CD.

**(1)**

**(Triangles on the same base and between the same parallels are equal in area.)**

Similarly, and are on the same base AC and between the same parallels XY and AC.

** (2)**

**(Triangles on the same base and between the same parallels are equal in area.)**

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