**In Figure, ar (DRC) = ar (DPC) and ar (BDP) = ar (ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.**

**Solution:**

ABCD and DCPR are two quadrilaterals.

It is given that ** (1)**

We can also note that and are on the same base DC. **(2)**

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

**(3)**

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

Similarly, it is given that ** (4)**

Subtracting **(1)** from **(4)**, we get

**(5)**

We can also note that and are on the same base CD. **(6)**

From **(5)** and **(6)**, we can say that ** (7)**

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

From **(3)** and **(7)**, we can say that both the quadrilaterals ABCD and DCPR are trapeziums**.**