Question

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

Step1: Recall parallel - line definition in 3D

In a cube, parallel lines are lines that lie in the same plane and do not intersect.

Step2: Analyze each option

• For $\overline{HI}$ and $\overline{IM}$: $\overline{HI}$ and $\overline{IM}$ are adjacent edges of a face of the cube. They intersect at point $I$, so they are not parallel.
• For $\overline{MN}$ and $\overline{GH}$: $\overline{MN}$ and $\overline{GH}$ are non - intersecting lines that lie in parallel planes of the cube. They are parallel.
• For $\overline{KL}$ and $\overline{LM}$: $\overline{KL}$ and $\overline{LM}$ are adjacent edges of a face of the cube. They intersect at point $L$, so they are not parallel.
• For $\overline{GK}$ and $\overline{LM}$: $\overline{GK}$ and $\overline{LM}$ are non - intersecting lines that lie in parallel planes of the cube. They are parallel.

Answer:

$\overline{MN}$ and $\overline{GH}$, $\overline{GK}$ and $\overline{LM}$