In the diagram provided, we are asked to identify three segments that are parallel to segment $HG$. To solve this, we need to consider the geometry of the prism and how different line segments relate to each other in terms of their orientation.

Step-by-step approach:

1. Identifying segment $HG$: Segment $HG$ is at the base of the prism, connecting points $H$ and $G$, which is a horizontal edge.

2. Finding parallel segments: Since the figure is a rectangular prism, the edges on opposite sides of the prism that are parallel to $HG$ should also be horizontal and run along the same direction.

   • Segment $EF$ is parallel to $HG$ because it is on the opposite face of the prism, connecting points $E$ and $F$ in a similar orientation.
   • Segment $AB$ is parallel to $HG$ because it connects the top vertices $A$ and $B$ in a horizontal manner, similar to $HG$.
   • Segment $DC$ is parallel to $HG$ as well, connecting the top vertices $D$ and $C$, again in the same horizontal orientation.

Thus, the three segments that are parallel to $HG$ are:

• $EF$
• $AB$
• $DC$

The correct answer is Option A: $EF$, $AB$, and $DC$.

Would you like more details on any part of this solution or the properties of parallel lines in prisms?

Related questions:

1. How do you determine when two line segments are parallel in 3D geometry?
2. What are the properties of a rectangular prism that help identify parallel edges?
3. Can a segment be parallel to a face instead of another segment in a prism?
4. How do perpendicular line segments differ from parallel ones in 3D shapes?
5. What role do parallel and perpendicular lines play in the geometry of prisms?

Tip: In any prism, segments that form edges of opposite parallel faces will always be parallel to each other.