Question

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

Explanation:

Step1: Recall parallel - line property in cube

In a cube, opposite edges are parallel.

Step2: Analyze each pair

• For $\overleftrightarrow{OR}$ and $\overleftrightarrow{KN}$: They are opposite edges of a face of the cube, so they are parallel.
• For $\overleftrightarrow{OR}$ and $\overleftrightarrow{PQ}$: They are opposite edges of a face of the cube, so they are parallel.
• For $\overleftrightarrow{NR}$ and $\overleftrightarrow{LP}$: They are opposite edges of a face of the cube, so they are parallel.
• For $\overleftrightarrow{NR}$ and $\overleftrightarrow{MQ}$: They are opposite edges of a face of the cube, so they are parallel.

Answer:

$\overleftrightarrow{OR}$ and $\overleftrightarrow{KN}$, $\overleftrightarrow{OR}$ and $\overleftrightarrow{PQ}$, $\overleftrightarrow{NR}$ and $\overleftrightarrow{LP}$, $\overleftrightarrow{NR}$ and $\overleftrightarrow{MQ}$