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In a $Δ A B C$ , if $L$ , if and $M$ and are points on $A B$ are points on and $A C$ and respectively such that $L M | | B C$ respectively such that . Then, $a r Δ A B M = a r Δ A C L$ . Then, .

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True

False

answer is A.

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Detailed Solution

Given that, in a

Δ A B C

, if

L

and

M

are points on

A B

and

A C

respectively.

L M | | B C

.
Compute the figure.
Question Image

The triangles

Δ L M B, Δ L M C

are on the same base

L M

.
And they are between the same parallels

L M, B C

.
And hence,

a r Δ L C M = a r Δ L B M

Add

a r (Δ A L M)

on both sides,

⇒ a r Δ L C M + Δ A L M = a r Δ L B M + Δ A L M

⇒ a r Δ A B M = a r Δ A C L

Hence, the statement is true.
Therefore, option 1 is correct.

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