Question

In ∆ABC, if L and M are the points on AB and AC respectively such that LM || BC, then prove that ar (∆LOB) = ar (∆MOC).

Answer 1

Given: In ∆ABC, L and M are two points on AB and AC, such that LM || BC.

To Prove: ar(∆LOB) = ar(∆MOC)

Proof: MB and LC intersect each other at O.

Since, ∆LBC and ∆MBC both lie on the same base BC and between the same parallel lines BC and LM

ar (∆LBC) = ar (∆MBC)

⇒ ar (∆LOB) + ar (∆BOC) = ar(∆MOC) + ar(∆BOC)

⇒ ar (∆LOB) = ar (∆MOC)

[Eliminating ar (∆BOC) from both sides]

Hence proved.