(Q21) Prove that a line joining the mid points of any two sides of a triangle is parallel to the third side. (Using converse of Basic proportionality theorem)

Solution :

Given : ∆ABC, D is the midpoint of AB and E is the midpoint of AC.

R.T.P : DE ∥ BC

Proof :

Since D is the midpoint of AB, we have AD = DB.

also 'E' is the midpoint of AC, we have AE = EC

From (1) and (2)

If a line divides any two sides of a triangle in the same ratio then it is parallel to the third side.

∴ DE ∥ BC by Basic proportionality theorem.

Hence Proved.