Question

which triangle is similar to △pru? △qrs △stu △ptq

Explanation:

Step1: Identify Vertical Angles

$\angle RSP$ and $\angle TSP$ (wait, actually $\angle R S P$ and $\angle T S U$? No, better: $\angle R S P$ and $\angle T S U$ are vertical angles? Wait, looking at the diagram, $\angle R S Q$ and $\angle T S U$? Wait, no, the triangles: $\triangle PRU$ and $\triangle PTQ$. Let's check angles. $\angle P$ is common to both $\triangle PRU$ and $\triangle PTQ$. Then, $\angle PRU$ and $\angle PTQ$? Wait, no, let's see: $\angle R$ and $\angle T$? Wait, no, the vertical angles at $S$: $\angle R S Q$ and $\angle T S U$ are vertical, but for similarity, AA (Angle-Angle) criterion. $\triangle PRU$ and $\triangle PTQ$: $\angle P$ is shared (common angle), and $\angle PRU$ and $\angle PTQ$? Wait, no, actually, $\angle R$ and $\angle T$? Wait, maybe I messed up. Wait, the correct approach: $\triangle PRU$ and $\triangle PTQ$: $\angle P$ is common, and $\angle PRS$ (wait, $\angle R$) and $\angle T$? No, better: $\triangle PRU$ and $\triangle PTQ$: $\angle P$ is common, and $\angle RSU$ (wait, no, the vertical angles at $S$: $\angle R S P$ and $\angle T S Q$? Wait, maybe the correct triangle is $\triangle PTQ$ because $\angle P$ is common, and $\angle PRU$ and $\angle PTQ$? Wait, no, let's use AA. If two angles are equal, triangles are similar. $\triangle PRU$ and $\triangle PTQ$: $\angle P$ is common, and $\angle R$ and $\angle T$? Wait, no, maybe the vertical angles at $S$: $\angle R S Q$ and $\angle T S U$ are equal, but for $\triangle PRU$ and $\triangle PTQ$, $\angle P$ is common, and $\angle PRU = \angle PTQ$ (if lines are such that $RQ$ and $TU$ are... Wait, maybe the correct answer is $\triangle PTQ$ because of AA similarity: common angle at $P$, and vertical angles or corresponding angles. So the triangle similar to $\triangle PRU$ is $\triangle PTQ$.

Answer:

$\triangle PTQ$