Question

s t 10 20 r 8 4 u p q not similar or not necessarily similar similar: △stu ~ △ by the select

Explanation:

Step1: Check Angle and Sides

In $\triangle STU$ and $\triangle QPR$ (assuming the angle at $U$ and $R$ are equal, vertical or included angles). The sides around the equal angle: For $\triangle STU$, sides are $SU = 10$, $TU = 20$; for $\triangle QPR$, sides are $QR = 4$, $PR = 8$.

Step2: Check Proportions

Calculate the ratios: $\frac{SU}{QR}=\frac{10}{4}=\frac{5}{2}$, $\frac{TU}{PR}=\frac{20}{8}=\frac{5}{2}$. Since the included angles are equal (vertical or given equal) and the sides around the angle are proportional, by SAS (Side - Angle - Side) similarity criterion, the triangles are similar. So $\triangle STU \sim \triangle QPR$ (or $\triangle RQP$ depending on labeling) by SAS similarity.

Answer:

Similar: $\triangle STU \sim \triangle QPR$ (or appropriate labeled triangle) by the SAS (Side - Angle - Side) Similarity Criterion.