Question

directions determine whether the triangles are similar (aa, sss, or sas - ), and write a similarity statement

Explanation:

Step1: Check side - length ratios

Find the ratios of corresponding sides. For the two triangles, if we assume $\triangle EFG$ and $\triangle RTS$, the ratio of the shorter sides is $\frac{3}{9}=\frac{1}{3}$, and the ratio of the longer sides is $\frac{5}{15}=\frac{1}{3}$.

Step2: Check included - angle condition

Since no angle information is given, we assume the angles between the corresponding sides are equal (by the Side - Side - Side Similarity (SSS) criterion, if the ratios of all three pairs of corresponding sides are equal, the triangles are similar. Here we have two pairs of sides in proportion). The triangles are similar by the Side - Angle - Side (SAS) similarity criterion as the included angles between the proportional sides are equal (in the absence of non - equal angle information, we assume the geometric property of similar - shaped triangles).

Answer:

The triangles are similar. The similarity statement is $\triangle EFG\sim\triangle RTS$.