Question

in the triangular prism shown below, which lines are parallel? select all that apply.
rs and rt
rs and op
oq and ps
or and op

Explanation:

Step1: Recall parallel - line concept in 3D

In a triangular prism, parallel lines are lines that lie in the same plane and never intersect.

Step2: Analyze each option

• For $\overrightarrow{RS}$ and $\overrightarrow{RT}$: They intersect at point $R$, so they are not parallel.
• For $\overrightarrow{RS}$ and $\overrightarrow{OP}$: In a triangular prism, the corresponding edges of the two bases are parallel. $\overrightarrow{RS}$ and $\overrightarrow{OP}$ are corresponding edges of the two bases, so they are parallel.
• For $\overrightarrow{OQ}$ and $\overrightarrow{PS}$: $\overrightarrow{OQ}$ and $\overrightarrow{PS}$ are parallel as they are opposite sides of a parallelogram - like face of the prism.
• For $\overrightarrow{OR}$ and $\overrightarrow{OP}$: They intersect at point $O$, so they are not parallel.

Answer:

$\overrightarrow{RS}$ and $\overrightarrow{OP}$, $\overrightarrow{OQ}$ and $\overrightarrow{PS}$