Question

In the given figure, LM CB and LN CD.
Prove that $\frac{AM}{AB}=\frac{AN}{AD}.$

Answer 1

$LM\parallel CB\mathrm{and}LN\parallel CD$

Therefore, applying Thales' theorem, we have:
$$\begin{gathered} \frac{AB}{AM}=\frac{AC}{AL}\mathrm{and}\frac{AD}{AN}=\frac{AC}{AL} \\ \Rightarrow \frac{AB}{AM}=\frac{AD}{AN} \\ \therefore \frac{AM}{AB}=\frac{AN}{AD} \end{gathered}$$
This completes the proof.