**P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC).**

**Solution:**

ABCD is a parallelogram. P is the point on side CD and Q is the point on side AD.

We need to show that ar(APB)=ar(BQC)

We can note that parallelogram ABCD and are on the same base BC and between the same parallels BC and AD. It means that ** (1)**

In the same way, parallelogram ABCD and are on the same base AB and between the same parallels AB and CD. It means that **(2)**

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

**Hence Proved**