**In figure, P is a point in the interior of a parallelogram ABCD. Show that **

**(i)**

**(ii)**

**[Hint: Through P, draw a line parallel to AB.]**

**Solution (i)**

ABCD is a parallelogram and P is a point present in parallelogram ABCD.

We need to show that** **

**Construction: **Draw a line EF passing through P which is parallel to AB. **(1)**

We also have ** (Because ABCD is a parallelogram) (2)**

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

** (A quadrilateral is a parallelogram if both the pairs of opposite sides are parallel)**

**Similarly, we can prove that EFCD is a parallelogram.**

So, we can notice that and parallelogram ABFE are on the same base AB and between the same parallels AB and EF.

** (3)**

Similarly, and parallelogram EFCD are on the same base CD and between the same parallels EF and CD.

**(4)**

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

**Solution (ii)**

We have already proved above that

**(5)**

Similarly, by drawing a line through P which is parallel to AD, we can show that

** (6)**

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