Question

in the cube shown below, which lines are parallel?

Explanation:

Step1: Recall parallel - line property in cube

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

Step2: Analyze each option

• For $\overleftrightarrow{HL}$ and $\overleftrightarrow{GH}$, they intersect at point $H$, so they are not parallel.
• For $\overleftrightarrow{GK}$ and $\overleftrightarrow{EH}$, they are skew - lines (not in the same plane and do not intersect), not parallel.
• For $\overleftrightarrow{IJ}$ and $\overleftrightarrow{GH}$, they are in parallel planes and do not intersect. In a cube, opposite edges are parallel. $\overleftrightarrow{IJ}$ and $\overleftrightarrow{GH}$ are opposite edges of the cube, so they are parallel.
• For $\overleftrightarrow{IL}$ and $\overleftrightarrow{GH}$, they are skew - lines, not parallel.

Answer:

$\overleftrightarrow{IJ}$ and $\overleftrightarrow{GH}$