Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
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.
[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.
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.