In the given figure, LM CB and LN CD.
Question:

In the given figure, LM  CB and LN  CD.

Prove that $\frac{A M}{A B}=\frac{A N}{A D}$.

Solution:

$L M \| C B$ and $L N \| C D$

Therefore, applying Thales’ theorem, we have:

$\frac{A B}{A M}=\frac{A C}{A L}$ and $\frac{A D}{A N}=\frac{A C}{A L}$

$\Rightarrow \frac{A B}{A M}=\frac{A D}{A N}$

$\therefore \frac{A M}{A B}=\frac{A N}{A D}$

This completes the proof.