To solve this problem, we are asked to identify three line segments that are parallel to line $\overline{HG}$ based on the given 3D figure. The figure appears to be a rectangular prism, with some lines parallel and perpendicular to each other.

Steps to solve:

1. Identify the line segment $\overline{HG}$:

   • $\overline{HG}$ is one of the horizontal edges of the rectangular prism, located at the bottom right corner, connecting points $H$ and $G$.

2. Determine the other parallel segments:

   • In a rectangular prism, the edges parallel to $\overline{HG}$ will be other horizontal edges of the same length and orientation.
   • Therefore, segments that run horizontally across the prism, on the same level as $\overline{HG}$, are the ones parallel to it.

3. Parallel segments:

   • $\overline{EF}$: This is the horizontal edge directly on the opposite side of $\overline{HG}$, connecting points $E$ and $F$.
   • $\overline{AB}$: The top horizontal edge, running parallel to $\overline{HG}$, connecting points $A$ and $B$.
   • $\overline{DC}$: The top horizontal edge on the opposite side from $\overline{HG}$, connecting points $D$ and $C$.

Answer:

The three segments parallel to $\overline{HG}$ are $\overline{EF}, \overline{AB}, \overline{DC}$.

Thus, the correct choice is: A) $\overline{EF}, \overline{AB}, \overline{DC}$.

Would you like more details on any part of the solution?

Here are 5 questions related to this concept:

1. How do you identify parallel lines in 3D figures like rectangular prisms?
2. What properties of a rectangular prism ensure that certain segments are parallel?
3. How would you find perpendicular segments in this figure?
4. What changes in this problem if the shape is not a rectangular prism?
5. How do you calculate the length of these parallel segments if given coordinates?

Tip: In 3D geometry, recognizing parallelism between line segments often involves finding corresponding edges of the same orientation in a prism or box-like figure.