in the cube 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 $\overleftrightarrow{FJ}$ and $\overleftrightarrow{CF}$

$\overleftrightarrow{FJ}$ and $\overleftrightarrow{CF}$ intersect at point F, so they are not skew.

Step3: Analyze $\overleftrightarrow{EF}$ and $\overleftrightarrow{DH}$

$\overleftrightarrow{EF}$ and $\overleftrightarrow{DH}$ are non - parallel and do not intersect. They are skew.

Step4: Analyze $\overleftrightarrow{HI}$ and $\overleftrightarrow{EF}$

$\overleftrightarrow{HI}$ and $\overleftrightarrow{EF}$ are parallel, so they are not skew.

Step5: Analyze $\overleftrightarrow{IJ}$ and $\overleftrightarrow{CG}$

$\overleftrightarrow{IJ}$ and $\overleftrightarrow{CG}$ are non - parallel and do not intersect. They are skew.

Answer:

$\overleftrightarrow{EF}$ and $\overleftrightarrow{DH}$, $\overleftrightarrow{IJ}$ and $\overleftrightarrow{CG}$