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.
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
But, we have AD = DB (Given)
Putting (2) in equation (1), we get
Therefore, E is the midpoint of side AC of ABC.