Question

determine whether the triangles are similar by aa-, sss-, sas-, or not similar.

Explanation:

Step1: List side length ratios

$\frac{SR}{QN} = \frac{44}{17}$, $\frac{ST}{QP} = \frac{55}{25} = \frac{11}{5}$, $\frac{RT}{NP} = \frac{37.4}{20} = \frac{187}{100}$

Step2: Simplify and compare ratios

$\frac{44}{17} \approx 2.588$, $\frac{11}{5}=2.2$, $\frac{187}{100}=1.87$
All ratios are not equal.

Step3: Check similarity criteria

SSS similarity requires all 3 side ratios equal; SAS needs 2 equal ratios + included angle; AA needs 2 equal angles. None are satisfied.

Answer:

The triangles are not similar.