Question

in the triangular pyramid shown below, which lines are skew? select all that apply. eg and fh eh and fg ef and gh fg and gh

Explanation:

Step1: Recall skew - line definition

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

Step2: Analyze each pair

1. For $\overrightarrow{EG}$ and $\overrightarrow{FH}$: They are non - parallel and do not intersect in the triangular pyramid, so they are skew.
2. For $\overrightarrow{EH}$ and $\overrightarrow{FG}$: They are non - parallel and do not intersect in the triangular pyramid, so they are skew.
3. For $\overrightarrow{EF}$ and $\overrightarrow{GH}$: They are non - parallel and do not intersect in the triangular pyramid, so they are skew.
4. For $\overrightarrow{FG}$ and $\overrightarrow{GH}$: They share a common point $G$, so they are not skew.

Answer:

$\overrightarrow{EG}$ and $\overrightarrow{FH}$, $\overrightarrow{EH}$ and $\overrightarrow{FG}$, $\overrightarrow{EF}$ and $\overrightarrow{GH}$