Question

determine if triangle lmn and triangle opq are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.)

Explanation:

Step1: Calculate the ratios of corresponding sides

For triangle \(LMN\) and \(OPQ\), we have:
\(\frac{NL}{OQ}=\frac{5}{10}=\frac{1}{2}\), \(\frac{MN}{PQ}=\frac{8}{16}=\frac{1}{2}\), \(\frac{LM}{OP}=\frac{6}{12}=\frac{1}{2}\)

Step2: Check the similarity criterion

Since \(\frac{NL}{OQ}=\frac{MN}{PQ}=\frac{LM}{OP}=\frac{1}{2}\), by the Side - Side - Side (SSS) similarity criterion, the two triangles are similar.

Answer:

Triangle \(LMN\) and triangle \(OPQ\) are similar. We know this because the ratios of their corresponding sides are equal (\(\frac{NL}{OQ}=\frac{MN}{PQ}=\frac{LM}{OP}=\frac{1}{2}\)), which satisfies the SSS (Side - Side - Side) similarity criterion.