Question

in the rectangular prism shown below, which lines are parallel? select all that apply.
image of a rectangular prism with vertices labeled q, r, s, t, u, v, w, x
options (with checkmarks): (overleftrightarrow{qt}) and (overleftrightarrow{vw}), (overleftrightarrow{rs}) and (overleftrightarrow{vw}), (overleftrightarrow{sw}) and (overleftrightarrow{tx}), (overleftrightarrow{qr}) and (overleftrightarrow{st})

Explanation:

Step1: Recall parallel lines in prism

In a rectangular prism, opposite edges are parallel.

Step2: Check each pair

• $\overline{QT}$ and $\overline{VW}$: Opposite vertical edges → parallel.
• $\overline{RS}$ and $\overline{VW}$: $\overline{RS} \parallel \overline{QT}$ (top face opposite edges), $\overline{QT} \parallel \overline{VW}$ → $\overline{RS} \parallel \overline{VW}$.
• $\overline{SW}$ and $\overline{TX}$: Opposite horizontal edges (bottom/side faces) → parallel.
• $\overline{QR}$ and $\overline{ST}$: Opposite top/side face edges → parallel.

Answer:

$\overline{QT}$ and $\overline{VW}$, $\overline{RS}$ and $\overline{VW}$, $\overline{SW}$ and $\overline{TX}$, $\overline{QR}$ and $\overline{ST}$