Question

in the triangular pyramid shown below, which lines are intersecting?
options: (overrightarrow{gi}) and (overrightarrow{fh}), (overrightarrow{fi}) and (overrightarrow{gh}), (overrightarrow{hi}) and (overrightarrow{fg}), (overrightarrow{fg}) and (overrightarrow{fh})

Explanation:

Step1: Recall intersecting lines definition

Intersecting lines share a common point.

Step2: Analyze each option

• For $\overrightarrow{GI}$ and $\overrightarrow{FH}$: They do not intersect in the pyramid.
• For $\overrightarrow{FI}$ and $\overrightarrow{GH}$: They do not intersect in the pyramid.
• For $\overrightarrow{HI}$ and $\overrightarrow{FG}$: They do not intersect in the pyramid.
• For $\overrightarrow{FG}$ and $\overrightarrow{FH}$: They share the common - point $F$, so they are intersecting.

Answer:

$\overrightarrow{FG}$ and $\overrightarrow{FH}$