Question

in the triangular prism shown below, which lines are parallel? mn and mo pr and mn pq and qr mp and nq

Explanation:

Step1: Recall parallel - line property in prism

In a triangular prism, corresponding edges of the parallel bases are parallel. Also, lateral - edges are parallel.

Step2: Analyze each option

• $\overrightarrow{MN}$ and $\overrightarrow{MO}$ share a common point $M$, so they are not parallel.
• $\overrightarrow{PR}$ and $\overrightarrow{MN}$ are not corresponding edges of parallel bases and are not lateral - edges, so they are not parallel.
• $\overrightarrow{PQ}$ and $\overrightarrow{QR}$ are adjacent sides of a triangular base, so they are not parallel.
• $\overrightarrow{MP}$ and $\overrightarrow{NQ}$ are lateral - edges of the triangular prism. Lateral - edges of a prism are parallel.

Answer:

$\overrightarrow{MP}$ and $\overrightarrow{NQ}$