**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.2 Question 7**

**7. Using Basic Proportionality theorem, prove that a line drawn through the midpoint of one side of a triangle parallel to another side bisects the third side.**

**Solution:**

**Given:** D is the midpoint of AB and DE BC.

**To prove:** E is the midpoint of AC.

**Proof: **It is given that DE BC. Therefore, by Basic Proportionality theorem, we can say that

**(1)**

But, we have AD = DB **(Given)**

**(2)**

Putting **(2) **in equation **(1), **we get

**Therefore, E is the midpoint of side AC of ABC.**

**Hence Proved**