Question

p q 4 10 r 5 15 6 t u not similar or not necessarily similar similar: △stu ~ △ by the select

Explanation:

Step1: Check Side Ratios

Calculate ratios of corresponding sides. For sides around the included angle:
$\frac{15}{10} = \frac{3}{2}$, $\frac{6}{4} = \frac{3}{2}$.

Step2: Check Included Angles

The included angles (at S and R) are equal (marked as congruent angles).

Step3: Apply SAS Similarity

By SAS (Side - Angle - Side) similarity criterion: if two sides of one triangle are proportional to two sides of another triangle, and the included angles are equal, triangles are similar. So $\triangle STU \sim \triangle QRP$ (or $\triangle PRQ$) by SAS similarity.

Answer:

Similar: $\triangle STU \sim \triangle QRP$ (or $\triangle PRQ$) by the SAS Similarity Criterion