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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.

Identify three segments parallel to HG using the figure shown. Assume lines and planes that appear to be parallel or perpendicular are parallel or perpendicular, respectively.

Learn how to identify parallel line segments in a prism by analyzing the geometric properties of the figure. This problem explores the concept of parallel lines, especially in 3D shapes such as prisms. Suitable for students in Grades 9-12.

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