Answered

At IDNLearn.com, find answers to your most pressing questions from experts and enthusiasts alike. Our experts provide timely, comprehensive responses to ensure you have the information you need.

Complete the proof.
\begin{tabular}{|l|l|}
\hline Statements & Reasons \\
\hline [tex]$AB = 3$[/tex], [tex]$BC = 5$[/tex], and [tex]$CA = 3.5$[/tex] & Given \\
[tex]$LM = 6.3$[/tex], [tex]$MN = 9$[/tex], and [tex]$NL = 5.4$[/tex] & Given \\
\hline [tex]$\frac{NL}{AB} = \frac{5.4}{3}$[/tex] & Corresponding sides of similar triangles \\
[tex]$\frac{MN}{BC} = \frac{9}{5}$[/tex] & Corresponding sides of similar triangles \\
[tex]$\frac{LM}{CA} = \frac{6.3}{3.5}$[/tex] & Corresponding sides of similar triangles \\
\hline [tex]$\frac{5.4}{3} = 1.8$[/tex] & Simplification \\
[tex]$\frac{9}{5} = 1.8$[/tex] & Simplification \\
[tex]$\frac{6.3}{3.5} = 1.8$[/tex] & Simplification \\
\hline [tex]$\frac{NL}{AB} = \frac{MN}{BC} = \frac{LM}{CA}$[/tex] & All ratios are equal \\
\hline [tex]$\triangle ABC \sim \triangle LNM$[/tex] & By the definition of similar triangles \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
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.
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.