Question

In the figure, if $ LM \left|\right| CB$ and $ LN \left|\right| CD$, prove that $ \frac{AM}{AB}=\frac{AN}{AD}$

Answer 1

Basic proportionality theorem:

In $△ABC$ , $LM\parallel CB$ is given

Therefore by basic proportionality theorem

$\frac{AM}{AB}=\frac{AL}{AC}$ …….(1)

In $△ACD,LN\parallel CD$ is given

Therefore by basic proportionality theorem

$\frac{AN}{AD}=\frac{AL}{AC}$ ………(2)

Now on comparing (1) and (2)

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

Hence it is proved that $\frac{AM}{AB}=\frac{AN}{AD}$