Question

in the triangular prism shown below, which lines are skew? select all that apply. lesson: parallel and perpendicular lines parts of three - dimensional figures not feeling ready yet? these can help: work it out parallel, perpendicular, and intersecting lines

Explanation:

Step1: Recall skew - lines definition

Skew lines are non - parallel and non - intersecting lines in 3 - D space.

Step2: Analyze each pair

• For $\overrightarrow{ST}$ and $\overrightarrow{VW}$: They are in different planes and do not intersect and are not parallel, so they are skew.
• For $\overrightarrow{SU}$ and $\overrightarrow{WX}$: They are in different planes and do not intersect and are not parallel, so they are skew.
• For $\overrightarrow{SU}$ and $\overrightarrow{VW}$: They are in different planes and do not intersect and are not parallel, so they are skew.
• For $\overrightarrow{ST}$ and $\overrightarrow{VX}$: $\overrightarrow{ST}$ and $\overrightarrow{VX}$ are in the same plane (the triangular face of the prism), so they are not skew.

Answer:

$\overrightarrow{ST}$ and $\overrightarrow{VW}$, $\overrightarrow{SU}$ and $\overrightarrow{WX}$, $\overrightarrow{SU}$ and $\overrightarrow{VW}$