Question

1. which segments in the picture are parallel?

○ $overline{hf}$ and $overline{de}$
○ $overline{ad}$ and $overline{ab}$
○ $overline{be}$ and $overline{gh}$
○ $overline{bc}$ and $overline{hf}$

Explanation:

Step1: Recall parallel - line definition

Parallel lines in 3 - D do not intersect and are in the same or parallel planes.

Step2: Analyze each option

• $\overline{HF}$ and $\overline{DE}$: They are not parallel as they are not in the same or parallel planes and their directions are different.
• $\overline{AD}$ and $\overline{AB}$: These are adjacent sides of a face, they intersect at point $A$, so they are not parallel.
• $\overline{BE}$ and $\overline{GH}$: In a prism - like structure, these two segments are in parallel planes and have the same direction. They do not intersect.
• $\overline{BC}$ and $\overline{HF}$: They are not parallel as they are not in the same or parallel planes and their directions are different.

Answer:

$\overline{BE}$ and $\overline{GH}$