Question

in the triangular prism shown below, which lines are parallel? select all that apply.

Explanation:

Step1: Recall parallel - line property in prism

In a triangular prism, corresponding edges of the two parallel bases are parallel, and lateral - edges are parallel to each other.

Step2: Analyze each option

• For $\overrightarrow{QR}$ and $\overrightarrow{ST}$: The two bases of the triangular prism are parallel triangles. $\overrightarrow{QR}$ and $\overrightarrow{ST}$ are corresponding sides of the two parallel bases, so $\overrightarrow{QR}\parallel\overrightarrow{ST}$.
• For $\overrightarrow{RS}$ and $\overrightarrow{QP}$: $\overrightarrow{RS}$ and $\overrightarrow{QP}$ are corresponding sides of the two parallel bases, so $\overrightarrow{RS}\parallel\overrightarrow{QP}$.
• For $\overrightarrow{PS}$ and $\overrightarrow{QT}$: $\overrightarrow{PS}$ and $\overrightarrow{QT}$ are lateral - edges of the triangular prism, so $\overrightarrow{PS}\parallel\overrightarrow{QT}$.
• For $\overrightarrow{OQ}$ and $\overrightarrow{RT}$: They are not parallel as they do not follow the parallel - edge rules of a triangular prism.

Answer:

$\overrightarrow{QR}$ and $\overrightarrow{ST}$, $\overrightarrow{RS}$ and $\overrightarrow{QP}$, $\overrightarrow{PS}$ and $\overrightarrow{QT}$