Question

in the rectangular prism shown below, which lines are parallel? dh and eh bf and fg dh and gh ae and bf

Explanation:

Step1: Recall parallel - line property

In a rectangular prism, parallel lines are lines that never intersect and are in the same or parallel planes.

Step2: Analyze each option

• For $\overleftrightarrow{DH}$ and $\overleftrightarrow{EH}$, they intersect at point $H$, so they are not parallel.
• For $\overleftrightarrow{BF}$ and $\overleftrightarrow{FG}$, they intersect at point $F$, so they are not parallel.
• For $\overleftrightarrow{DH}$ and $\overleftrightarrow{GH}$, they intersect at point $H$, so they are not parallel.
• For $\overleftrightarrow{AE}$ and $\overleftrightarrow{BF}$, they are in parallel planes (the left - hand and right - hand faces of the rectangular prism) and do not intersect. They are parallel.

Answer:

$\overleftrightarrow{AE}$ and $\overleftrightarrow{BF}$