To solve the problem in the image:

The figure is a rectangular prism. The task is to determine how many lines in the prism are parallel to $\overline{HG}$.

Step-by-step Solution:

1. $\overline{HG}$ is one of the edges along the bottom face of the prism. Lines parallel to $\overline{HG}$ are also horizontal lines and run along the same direction.

2. In a rectangular prism, each edge has three sets of parallel edges. These correspond to the three dimensions (length, width, height).

3. Edges parallel to $\overline{HG}$ must be horizontal and align with the same direction:

   • $\overline{EF}$: directly opposite $\overline{HG}$ on the bottom face.
   • $\overline{AB}$: top face of the prism.
   • $\overline{CD}$: opposite to $\overline{AB}$, on the top face.

   These four edges ($\overline{HG}, \overline{EF}, \overline{AB}, \overline{CD}$) are all parallel to each other.

Answer:

C. 4

Let me know if you would like further explanation!

Follow-up Questions:

1. Can you identify the other sets of parallel edges in the rectangular prism?
2. Why does a rectangular prism have three distinct sets of parallel lines?
3. What is the difference between parallel and perpendicular lines in 3D geometry?
4. How would the count change if the prism were irregular rather than rectangular?
5. Can you describe the relationship between the diagonals and parallel edges in this figure?

Tip: When working with 3D geometry, visualizing or sketching each face separately can help identify relationships like parallelism or perpendicularity!