Question

in the triangular prism shown below, which lines are skew? select all that apply.

Explanation:

Step1: Recall skew - lines definition

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

Step2: Analyze each pair

• For $\overrightarrow{CF}$ and $\overrightarrow{GH}$: They are non - parallel and do not intersect, so they are skew.
• For $\overrightarrow{DE}$ and $\overrightarrow{FG}$: They are non - parallel and do not intersect, so they are skew.
• For $\overrightarrow{CE}$ and $\overrightarrow{FG}$: They are non - parallel and do not intersect, so they are skew.
• For $\overrightarrow{DE}$ and $\overrightarrow{FH}$: They are non - parallel and do not intersect, so they are skew.

Answer:

$\overrightarrow{CF}$ and $\overrightarrow{GH}$, $\overrightarrow{DE}$ and $\overrightarrow{FG}$, $\overrightarrow{CE}$ and $\overrightarrow{FG}$, $\overrightarrow{DE}$ and $\overrightarrow{FH}$