Question

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

Explanation:

Step1: Recall parallel - line definition in 3D

Parallel lines in 3D are lines that lie in the same plane and do not intersect.

Step2: Analyze each pair

• For $\overrightarrow{QT}$ and $\overrightarrow{RU}$: They are not parallel as they are skew lines (not in the same plane and do not intersect).
• For $\overrightarrow{PQ}$ and $\overrightarrow{QR}$: They are adjacent sides of a triangle - shaped face, so they are not parallel (they intersect at point $Q$).
• For $\overrightarrow{PR}$ and $\overrightarrow{SU}$: In a triangular prism, the corresponding edges of the parallel bases are parallel. $\overrightarrow{PR}$ and $\overrightarrow{SU}$ are corresponding edges of the parallel triangular bases, so they are parallel.
• For $\overrightarrow{QR}$ and $\overrightarrow{TU}$: These are also corresponding edges of the parallel triangular bases, so they are parallel.

Answer:

$\overrightarrow{PR}$ and $\overrightarrow{SU}$, $\overrightarrow{QR}$ and $\overrightarrow{TU}$