Question

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

Explanation:

Step1: Recall parallel - line property

In a triangular prism, parallel lines are lines that never intersect and are in the same or parallel planes.

Step2: Analyze each option

• For $\overrightarrow{LO}$ and $\overrightarrow{NQ}$: In a triangular prism, these lines are in parallel planes and have the same direction, so they are parallel.
• For $\overrightarrow{PQ}$ and $\overrightarrow{MP}$: These lines intersect at point $P$, so they are not parallel.
• For $\overrightarrow{LM}$ and $\overrightarrow{NQ}$: They are in parallel planes and have the same direction, so they are parallel.
• For $\overrightarrow{OQ}$ and $\overrightarrow{OP}$: These lines intersect at point $O$, so they are not parallel.

Answer:

$\overrightarrow{LO}$ and $\overrightarrow{NQ}$, $\overrightarrow{LM}$ and $\overrightarrow{NQ}$