**If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that**

**.**

**Solution:**

It is given that ABCD is a parallelogram. E, F, G and H are respectively the mid-points of the sides of a given parallelogram ABCD. **Join GE.**

We have **(Opposite sides of parallelogram are equal)**

**(1)**

We also have because . ** (Opposite sides of parallelogram are equal) (2)**

From **(1)** and** (2)**, we can say that **EBCG is a parallelogram**.

**(A quadrilateral is a parallelogram if one pair of opposite sides is equal and parallel.)**

We can clearly see that and parallelogram EBCG are on the same base and between same parallels.

**(3)**

Similarly, we have ** (4)**

Adding** (3)** and **(4)**, we get