# Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX)

**Solution:**

We know that theorem 6.1 states that “If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio (Basic Proportionality theorem)”.

In ΔABC, D is the midpoint of AB

Therefore,

AD = BD

AD/BD = 1

Now,

DE || BC

⇒ AE/EC = AD/BD [Theorem 6.1]

⇒ AE/EC = 1

Hence, E is the midpoint of AC.

**Video Solution:**

## Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX)

### Class 10 Maths NCERT Solutions - Chapter 6 Exercise 6.2 Question 7:

Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX)

Since E is the midpoint of AC. Hence it is proved that a line drawn through the midpoint of one side of a triangle parallel to another side bisects the third side.