Question 6
In $Δ A B C$ , if L and M are the points on AB and AC, respectively such that LM || BC. Prove that $a r (Δ L O B) = a r (Δ M O C)$ .

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Solution

We know that triangles on the same base and between the same parallels are equal in area.
Hence, $Δ$ LBC and $Δ$ MBC lie on the same base BC and between the same parallels BC and LM.
So, $a r (Δ L B C) = a r (Δ M B C)$
$\Rightarrow a r (Δ L O B) + a r (Δ B O C) = a r (Δ M O C) + a r (Δ B O C)$
On eliminating $a r (Δ B O C)$ from both sides, we get,
$a r (Δ L O B) = a r (Δ M O C)$

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Question 6 In ΔABC, if L and M are the points on AB and AC, respectively such that LM || BC. Prove that ar(ΔLOB)=ar(ΔMOC).

Question 6
In $Δ A B C$ , if L and M are the points on AB and AC, respectively such that LM || BC. Prove that $a r (Δ L O B) = a r (Δ M O C)$ .