Question

in the cube shown below, which lines are parallel? select all that apply. hk and mn, hi and no, ij and lo, jk and no

Explanation:

Step1: Recall parallel - line property in a cube

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

Step2: Analyze each pair

• For $\overrightarrow{HK}$ and $\overrightarrow{MN}$: They are opposite edges of the same - type face (square face) of the cube. They are parallel.
• For $\overrightarrow{HI}$ and $\overrightarrow{NO}$: $\overrightarrow{HI}$ and $\overrightarrow{NO}$ are parallel because they are opposite edges of parallel square - shaped faces of the cube.
• For $\overrightarrow{IJ}$ and $\overrightarrow{LO}$: They are not parallel. They are skew lines (not in the same plane and do not intersect).
• For $\overrightarrow{JK}$ and $\overrightarrow{NO}$: They are not parallel. They are skew lines.

Answer:

$\overrightarrow{HK}$ and $\overrightarrow{MN}$, $\overrightarrow{HI}$ and $\overrightarrow{NO}$