Question

in the triangular prism shown below, which lines are parallel? select all that apply.
rs and op
pq and st
oq and op
or and qt

Explanation:

Step1: Recall parallel - line property in prism

In a triangular prism, parallel lines are those that lie in parallel planes and do not intersect.

Step2: Analyze each pair

• For $\overrightarrow{RS}$ and $\overrightarrow{OP}$: They are in parallel planes and do not intersect, so they are parallel.
• For $\overrightarrow{PQ}$ and $\overrightarrow{ST}$: They are in parallel planes and do not intersect, so they are parallel.
• For $\overrightarrow{OQ}$ and $\overrightarrow{OP}$: They are in the same base - plane and share a common point $O$, so they are not parallel.
• For $\overrightarrow{OR}$ and $\overrightarrow{QT}$: They are in parallel planes and do not intersect, so they are parallel.

Answer:

$\overrightarrow{RS}$ and $\overrightarrow{OP}$, $\overrightarrow{PQ}$ and $\overrightarrow{ST}$, $\overrightarrow{OR}$ and $\overrightarrow{QT}$