Question

determine if triangle pqr and triangle stu are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.) answer the triangles are similar because

Explanation:

Step1: Calculate the ratios of corresponding sides

For triangle \(RQP\) and \(STU\), we have the following side - length ratios:
\(\frac{RQ}{ST}=\frac{13}{39}=\frac{1}{3}\), \(\frac{QP}{TU}=\frac{11}{33}=\frac{1}{3}\), \(\frac{PR}{US}=\frac{19}{57}=\frac{1}{3}\)

Step2: Check the similarity condition

By the Side - Side - Side (SSS) similarity criterion, if the ratios of the corresponding sides of two triangles are equal, then the two triangles are similar.

Answer:

The triangles are similar because the ratios of their corresponding sides are equal (\(\frac{RQ}{ST}=\frac{QP}{TU}=\frac{PR}{US}=\frac{1}{3}\)) and by the SSS (Side - Side - Side) similarity criterion.