Question

in the rectangular prism shown below, which lines are parallel? ij and kl, hi and jn, hi and ij, ij and lm

Explanation:

Step1: Recall parallel - line property in rectangular 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 $\overrightarrow{IJ}$ and $\overrightarrow{KL}$, they are opposite sides of a rectangular face of the prism, so they are parallel.
• $\overrightarrow{HI}$ and $\overrightarrow{JN}$ are not parallel as they are in non - parallel planes and will not have the same direction.
• $\overrightarrow{HI}$ and $\overrightarrow{IJ}$ are adjacent sides of a face, so they are not parallel.
• $\overrightarrow{IJ}$ and $\overrightarrow{LM}$ are not parallel as they are in non - parallel planes.

Answer:

$\overrightarrow{IJ}$ and $\overrightarrow{KL}$