Question

in the rectangular prism shown below, which lines are parallel?

Explanation:

Step1: Recall parallel - line property in rectangular prism

In a rectangular prism, opposite edges are parallel.

Step2: Analyze each option

• For $\overleftrightarrow{RS}$ and $\overleftrightarrow{TW}$: They are opposite edges on the top - and bottom - faces respectively, so they are parallel.
• For $\overleftrightarrow{PT}$ and $\overleftrightarrow{RS}$: They are not parallel. $\overleftrightarrow{PT}$ is a vertical edge and $\overleftrightarrow{RS}$ is a horizontal edge on the top - face.
• For $\overleftrightarrow{QU}$ and $\overleftrightarrow{RV}$: They are not parallel.
• For $\overleftrightarrow{QR}$ and $\overleftrightarrow{TU}$: They are not parallel.

Answer:

$\overleftrightarrow{RS}$ and $\overleftrightarrow{TW}$