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 bases are parallel and lateral - edges are parallel to each other.

Step2: Analyze each option

• For $\overrightarrow{LO}$ and $\overrightarrow{MP}$: They are not parallel. $\overrightarrow{LO}$ is an edge in the upper - base triangle and $\overrightarrow{MP}$ is a lateral edge.
• For $\overrightarrow{MP}$ and $\overrightarrow{NQ}$: In a triangular prism, lateral edges are parallel. $\overrightarrow{MP}$ and $\overrightarrow{NQ}$ are lateral edges, so they are parallel.
• For $\overrightarrow{OQ}$ and $\overrightarrow{LN}$: They are not parallel. $\overrightarrow{OQ}$ is a non - corresponding edge between the bases and $\overrightarrow{LN}$ is an edge in the upper - base triangle.
• For $\overrightarrow{PQ}$ and $\overrightarrow{MN}$: Corresponding edges of the two bases of a triangular prism are parallel. $\overrightarrow{PQ}$ and $\overrightarrow{MN}$ are corresponding edges of the two bases, so they are parallel.

Answer:

$\overrightarrow{MP}$ and $\overrightarrow{NQ}$, $\overrightarrow{PQ}$ and $\overrightarrow{MN}$