Question

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

Explanation:

Step1: Recall parallel - line property in 3D

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

Step2: Analyze pairs of lines

• For $\overrightarrow{TX}$ and $\overrightarrow{UY}$: They are in parallel planes and do not intersect, so they are parallel.
• For $\overrightarrow{RV}$ and $\overrightarrow{UY}$: In a rectangular prism, opposite - side edges are parallel. $\overrightarrow{RV}$ and $\overrightarrow{UY}$ are opposite - side edges of parallel rectangular faces, so they are parallel.
• For $\overrightarrow{ST}$ and $\overrightarrow{TX}$: They intersect at point $T$, so they are not parallel.
• For $\overrightarrow{XY}$ and $\overrightarrow{UY}$: They intersect at point $Y$, so they are not parallel.

Answer:

$\overrightarrow{TX}$ and $\overrightarrow{UY}$, $\overrightarrow{RV}$ and $\overrightarrow{UY}$