# Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX)

**Solution:**

We know that theorem 6.2 tells us if a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. (Converse of Basic Proportionality theorem)

In ΔABC,

D is the midpoint of AB

⇒ AD = BD

AD/BD = 1............ (i)

E is the midpoint of AC

AE = CE

⇒ AE/CE = 1........ (ii)

From equations (i) and (ii)

AD/BD = AE/CE = 1

AD/BD = AE/CE

In ΔABC, according to theorem 6.2 (Converse of Basic Proportionality theorem),

Since, AD/BD = AE/CE

Thus, DE || BC

Hence, proved.

**Video Solution:**

## Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX)

### Class 10 Maths NCERT Solutions - Chapter 6 Exercise 6.2 Question 8:

**Summary:**

Using Theorem 6.2, we have proved that the line joining the mid-points of any two sides of a triangle is parallel to the third side.