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State True or False.
In the given figure, if LM || CB and LN || CD, then $A M A B = A N A D$ .

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True

False

answer is A.

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Detailed Solution

Given that, LM || CB and LN || CD, in the following figure.
Question Image

We know Basic proportionality theorem (BPT), says that if a line is drawn parallel to one side of a triangle that intersects the other two sides in distinct points, then the other two sides are divided in the same ratio.
In

Δ A B C

, LM || CB. So, by using BPT

⇒ A M M B = A L L C

-----[1]
We also know that LN||CD.
In

Δ A D C

, using BPT we get

A N N D = A L L C

-----[2]
From [1] and [2], we get

A M M B = A N N D

On reciprocating both sides and then adding 1 to them, we get

M B A M + 1 = N D A N + 1 ⇒ A M + M B A M = A N + N D A N

Now,
AM+MB=AB and AN+ND=AD

⇒ A M A B = A N A D

The solution is the same as the given statement.
Hence, the statement is true.
Therefore, the correct option is 1.

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