Question

in the triangular prism shown below, which lines are parallel? ij and fg hj and ij eg and eh hj and ef

Explanation:

Step1: Recall parallel - line definition in 3 - D

Parallel lines in 3 - D are lines that lie in the same plane and do not intersect.

Step2: Analyze each option

• For $\overrightarrow{IJ}$ and $\overrightarrow{FG}$: In a triangular prism, the side - faces are parallelograms. The lines $\overrightarrow{IJ}$ and $\overrightarrow{FG}$ are opposite sides of the parallelogram - shaped side - face, so they are parallel.
• For $\overrightarrow{HJ}$ and $\overrightarrow{IJ}$: They intersect at point $J$, so they are not parallel.
• For $\overrightarrow{EG}$ and $\overrightarrow{EH}$: They intersect at point $E$, so they are not parallel.
• For $\overrightarrow{HJ}$ and $\overrightarrow{EF}$: They are not in the same plane, so they are not parallel.

Answer:

$\overrightarrow{IJ}$ and $\overrightarrow{FG}$