Question

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

answer attempt 1 out of 3

the triangles similar.

Explanation:

Step1: Calculate the ratios of corresponding sides

For triangle \(OPQ\) and \(RST\), \(\frac{OP}{RS}=\frac{99}{81}=\frac{11}{9}\), \(\frac{OQ}{RT}=\frac{88}{72}=\frac{11}{9}\), \(\frac{PQ}{ST}=\frac{88}{72}=\frac{11}{9}\)

Step2: Check the similarity condition

Since the ratios of all corresponding sides are equal (\(\frac{OP}{RS}=\frac{OQ}{RT}=\frac{PQ}{ST}=\frac{11}{9}\)), by the Side - Side - Side (SSS) similarity criterion, the two triangles are similar.

Answer:

The triangles are similar.