(Q20) Prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Using Basic proportionality theorem).

Solution :

Given : In ∆ABC; D is the mid-point of AB.

R.T.P : E is the midpoint of AC.

Proof : DE ∥ BC (given)

Also given 'D' is mid point of AB.

Then AD = DB.

AE =

∴ 'E' is midpoint of AC.

∴ The line bisects the third side AC.

Hence Proved.