In the given figure, if $LM \| CB$ and $LN \| CD$.
Prove that $ \frac{\mathbf{A M}}{\mathbf{A B}}=\frac{\mathbf{A N}}{\mathbf{A D}} $
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Given:

$LM \| CB$ and $LN \| CD$.

To do:

We have to prove that \( \frac{\mathbf{A M}}{\mathbf{A B}}=\frac{\mathbf{A N}}{\mathbf{A D}} \)

Solution:

We know that,

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

In $\triangle ABC, LM \| CB$,

This implies,

$\frac{AM}{AB}=\frac{AL}{AC}$.........(i)

In $\triangle ADC, LN \| CD$,

This implies,

$\frac{AN}{AD}=\frac{AL}{AC}$.........(ii)

From (i) and (ii), we get,

$\frac{AM}{AB}=\frac{AN}{AD}$

Hence proved.

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Updated on: 10-Oct-2022

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