Question

select
not similar or not necessarily similar
similar:
△stu ~ △□ by the
select
explanation check

Explanation:

Step1: Identify the included angles

In $\triangle STU$ and $\triangle RQP$, $\angle T$ and $\angle Q$ are the included angles (both are marked as equal, likely right angles or congruent angles from the diagram).

Step2: Calculate the ratios of the sides

For $\triangle STU$: $ST = 10$, $TU = 25$
For $\triangle RQP$: $RQ = 8$, $QP = 20$

Calculate the ratios:
$\frac{ST}{RQ} = \frac{10}{8} = \frac{5}{4}$
$\frac{TU}{QP} = \frac{25}{20} = \frac{5}{4}$

Since the ratios of the two sides are equal and the included angles are congruent, by the SAS (Side - Angle - Side) Similarity Criterion, the triangles are similar. The correspondence of the vertices: $S$ corresponds to $R$, $T$ corresponds to $Q$, $U$ corresponds to $P$, so $\triangle STU \sim \triangle RQP$.

Answer:

Similar: $\triangle STU \sim \triangle RQP$ by the SAS Similarity Criterion