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 $\overleftrightarrow{TV}$ and $\overleftrightarrow{UX}$: They are in different planes and do not intersect and are not parallel.
• For $\overleftrightarrow{TW}$ and $\overleftrightarrow{VY}$: They are in different planes, non - intersecting and non - parallel.
• For $\overleftrightarrow{TV}$ and $\overleftrightarrow{VY}$: They are in different planes, non - intersecting and non - parallel.
• For $\overleftrightarrow{WY}$ and $\overleftrightarrow{WX}$: $\overleftrightarrow{WY}$ and $\overleftrightarrow{WX}$ intersect at point $W$, so they are not skew.

Answer:

$\overleftrightarrow{TV}$ and $\overleftrightarrow{UX}$, $\overleftrightarrow{TW}$ and $\overleftrightarrow{VY}$, $\overleftrightarrow{TV}$ and $\overleftrightarrow{VY}$