Question

in the rectangular prism shown below, which lines are parallel? fj and eh, gk and hl, gk and eh, ij and jk

Explanation:

Step1: Recall parallel - line property in prism

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

Step2: Analyze each option

• For $\overrightarrow{FJ}$ and $\overrightarrow{EH}$: $\overrightarrow{FJ}$ and $\overrightarrow{EH}$ are not parallel as they are not in the same or parallel planes in the way required for parallel lines in a rectangular - prism.
• For $\overrightarrow{GK}$ and $\overrightarrow{HL}$: In a rectangular prism, opposite edges are parallel. $\overrightarrow{GK}$ and $\overrightarrow{HL}$ are opposite edges. They are in parallel planes and will never intersect.
• For $\overrightarrow{GK}$ and $\overrightarrow{EH}$: $\overrightarrow{GK}$ and $\overrightarrow{EH}$ are not parallel as they are not in the same or parallel planes in the way required for parallel lines in a rectangular - prism.
• For $\overrightarrow{IJ}$ and $\overrightarrow{JK}$: $\overrightarrow{IJ}$ and $\overrightarrow{JK}$ are adjacent edges and intersect at point $J$, so they are not parallel.

Answer:

$\overrightarrow{GK}$ and $\overrightarrow{HL}$