## Summary

The parallelograms are on the same base and between the same parallels.

Area of a Parallelogram = b × h

In both parallelograms:

• The bases are equal.

• The heights are equal.

Area of parallelogram ABCD = Area of parallelogram ABGH.

Parallelograms on the same base and between the same parallels are equal in area.

**Theorem:**

Prove that the area of the triangle is equal to half the area of the parallelogram, if they are on the same base and are between the same parallels.

Given:

Δ ABP and parallelogram ABCD are on same base AB and between the same parallels AB and PC.

To Prove: ar (ΔABP) =1/2 ar ( ||gm ABCD)

Construction: Draw BQ || AP

Proof:

ar ( ||gm ABQP) = ar ( || gm ABCD (Parallelograms on the same base and between the same parallels are equal in area.)

Δ ABP ≅ Δ BQP

ar (Δ ABP) = ar (Δ BQP)

ar (Δ ABP) = (½) ar (|| gm ABQP)

ar (Δ ABP) = (½) ar (|| gm ABCD).