Question

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

Explanation:

Step1: Recall skew - line definition

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

Step2: Analyze each pair

• For $\overleftrightarrow{RU}$ and $\overleftrightarrow{ST}$: They are non - parallel and do not intersect in the triangular pyramid, so they are skew.
• For $\overleftrightarrow{RS}$ and $\overleftrightarrow{ST}$: They intersect at point $S$, so they are not skew.
• For $\overleftrightarrow{RS}$ and $\overleftrightarrow{TU}$: They are non - parallel and do not intersect in the triangular pyramid, so they are skew.
• For $\overleftrightarrow{RS}$ and $\overleftrightarrow{SU}$: They intersect at point $S$, so they are not skew.

Answer:

$\overleftrightarrow{RU}$ and $\overleftrightarrow{ST}$, $\overleftrightarrow{RS}$ and $\overleftrightarrow{TU}$