Question

Prove that a line joining the mid points of any two sides of a triangle is parallel to the third side.

Answer 1

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 

⇒ \(\frac{AD}{DB}\) = 1 ……. (1) 

also ‘E’ is the midpoint of AC, we have AE = EC ⇒ \(\frac{AE}{EC}\) = 1 ……. (2) 

From (1) and (2)

 \(\frac{AD}{DB}=\frac{AE}{EC}\)

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.