Question

in the cube shown below, which lines are skew? select all that apply.
lesson: parallel and perpendicular lines
parts of three - dimensional figures
not feeling ready yet? these can help:
work it out
parallel, perpendicular, and intersecting lines

Explanation:

Step1: Recall skew - line definition

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

Step2: Analyze each pair

• $\overleftrightarrow{GI}$ and $\overleftrightarrow{EI}$: They intersect at point $I$, so they are not skew.
• $\overleftrightarrow{DE}$ and $\overleftrightarrow{EF}$: They intersect at point $E$, so they are not skew.
• $\overleftrightarrow{EI}$ and $\overleftrightarrow{GH}$: They are non - parallel and do not intersect. They are skew.
• $\overleftrightarrow{IJ}$ and $\overleftrightarrow{CF}$: They are non - parallel and do not intersect. They are skew.

Answer:

$\overleftrightarrow{EI}$ and $\overleftrightarrow{GH}$, $\overleftrightarrow{IJ}$ and $\overleftrightarrow{CF}$