Question

In the Figure, if $LM\parallel CB$ and $LN\parallel CD$, prove that $\frac{AM}{AB}=\frac{AN}{AD}$.

Answer 1

In $\Delta ABC$, as $LM\parallel BC$, so by basic proportionality theorem,

$\frac{AL}{AC}=\frac{AM}{AB}$ ........... $\left(1\right)$

In $\Delta ADC$, as $LN\parallel CD$, so by basic proportionality theorem,

$\frac{AL}{AC}=\frac{AN}{AD}$ ........... $\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right),$

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