Question

in the cube shown below, which lines are parallel? ps and mn nr and pq nr and mn mn and mq

Explanation:

Step1: Recall parallel - line property in cube

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

Step2: Analyze each option

• For $\overleftrightarrow{PS}$ and $\overleftrightarrow{MN}$: $\overleftrightarrow{PS}$ and $\overleftrightarrow{MN}$ are in parallel planes and do not intersect, so they are parallel.
• For $\overleftrightarrow{NR}$ and $\overleftrightarrow{PQ}$: $\overleftrightarrow{NR}$ and $\overleftrightarrow{PQ}$ are skew lines (not in the same plane and do not intersect).
• For $\overleftrightarrow{NR}$ and $\overleftrightarrow{MN}$: $\overleftrightarrow{NR}$ and $\overleftrightarrow{MN}$ intersect at point $N$.
• For $\overleftrightarrow{MN}$ and $\overleftrightarrow{MQ}$: $\overleftrightarrow{MN}$ and $\overleftrightarrow{MQ}$ intersect at point $M$.

Answer:

$\overleftrightarrow{PS}$ and $\overleftrightarrow{MN}$