Question

in the triangular prism shown below, which lines are parallel? select all that apply. the options are: \overleftrightarrow{pr} and \overleftrightarrow{su}, \overleftrightarrow{ps} and \overleftrightarrow{ru}, \overleftrightarrow{ps} and \overleftrightarrow{qt}, \overleftrightarrow{qt} and \overleftrightarrow{ru}

Explanation:

Step1: Analyze prism properties

A triangular prism has two congruent triangular bases and three rectangular lateral faces. Opposite edges of rectangles are parallel.

Step2: Check each option

• $\overline{PR}$ and $\overline{SU}$: They are corresponding edges of the two triangular bases, so parallel.
• $\overline{PS}$ and $\overline{RU}$: They are opposite edges of rectangle $PSUR$, so parallel.
• $\overline{PS}$ and $\overline{QT}$: $\overline{PS}$ is a lateral edge, $\overline{QT}$ is a segment inside the top base—they are not parallel.
• $\overline{QT}$ and $\overline{RU}$: $\overline{QT}$ is inside the top base, $\overline{RU}$ is a lateral edge—they are not parallel.

Answer:

A. $\overline{PR}$ and $\overline{SU}$, B. $\overline{PS}$ and $\overline{RU}$