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
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