Certainly! Let's complete the proof step-by-step.
[tex]\[
\begin{tabular}{|l|l|}
\hline
\textbf{Statements} & \textbf{Reasons} \\
\hline
$AB=3, BC=5$, and $CA=3.5$ & Given \\
$LM=6.3, MN=9$, and $NL=5.4$ & Given \\
\hline
$\frac{NL}{AB}=\frac{5.4}{3}$ & Definition of ratio \\
$\frac{MN}{BC}=\frac{9}{5}$ & Substitution property of equality \\
$\frac{LM}{CA}=\frac{6.3}{3.5}$ & Definition of ratio \\
\hline
$\frac{5.4}{3}=1.8$ & Division of values \\
$\frac{9}{5}=1.8$ & Division of values \\
$\frac{6.3}{3.5}=1.8$ & Division of values \\
\hline
$\frac{NL}{AB}=\frac{MN}{BC}=\frac{LM}{CA}$ & Transitive property of equality (if all ratios are equal) \\
\hline
$\triangle ABC \sim \triangle LNM$ & If corresponding side lengths of two triangles are in proportion, then the triangles are similar (by the SSS similarity criterion) \\
\hline
\end{tabular}
\][/tex]
Thus, we have demonstrated that triangles [tex]\( \triangle ABC \)[/tex] and [tex]\( \triangle LNM \)[/tex] are similar because the ratio of their corresponding sides is equal.
