Question

in the rectangular prism shown below, which lines are parallel? select all that apply.

Explanation:

Step1: Recall parallel - line property in rectangular prism

In a rectangular prism, lines that do not intersect and are in the same or parallel planes are parallel.

Step2: Analyze $\overline{PQ}$ and $\overline{NO}$

$\overline{PQ}$ and $\overline{NO}$ are in parallel planes and do not intersect, so they are parallel.

Step3: Analyze $\overline{LM}$ and $\overline{NO}$

$\overline{LM}$ and $\overline{NO}$ are in the same plane (a rectangular face) and do not intersect, so they are parallel.

Step4: Analyze $\overline{PQ}$ and $\overline{LO}$

$\overline{PQ}$ and $\overline{LO}$ are in parallel planes and do not intersect, so they are parallel.

Step5: Analyze $\overline{KO}$ and $\overline{LP}$

$\overline{KO}$ and $\overline{LP}$ are in parallel planes and do not intersect, so they are parallel.

Answer:

$\overline{PQ}$ and $\overline{NO}$, $\overline{LM}$ and $\overline{NO}$, $\overline{PQ}$ and $\overline{LO}$, $\overline{KO}$ and $\overline{LP}$