Question

in the rectangular prism shown below, which lines are skew? select all that apply. xy and tx st and rv rs and ru ru and wx

Explanation:

Step1: Recall skew - lines definition

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

Step2: Analyze $\overleftrightarrow{XY}$ and $\overleftrightarrow{TX}$

$\overleftrightarrow{XY}$ and $\overleftrightarrow{TX}$ intersect at point $X$, so they are not skew.

Step3: Analyze $\overleftrightarrow{ST}$ and $\overleftrightarrow{RV}$

$\overleftrightarrow{ST}$ and $\overleftrightarrow{RV}$ are non - parallel and do not intersect. They are in different planes and are skew.

Step4: Analyze $\overleftrightarrow{RS}$ and $\overleftrightarrow{RU}$

$\overleftrightarrow{RS}$ and $\overleftrightarrow{RU}$ intersect at point $R$, so they are not skew.

Step5: Analyze $\overleftrightarrow{RU}$ and $\overleftrightarrow{WX}$

$\overleftrightarrow{RU}$ and $\overleftrightarrow{WX}$ are non - parallel and do not intersect. They are in different planes and are skew.

Answer:

$\overleftrightarrow{ST}$ and $\overleftrightarrow{RV}$, $\overleftrightarrow{RU}$ and $\overleftrightarrow{WX}$