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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) \( \overline{EF}, \overline{AB}, \overline{DC} \)**.

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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.

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 segments that are parallel in a 3D rectangular prism. This problem demonstrates the concept of parallelism in geometry using line segments HG, EF, AB, and DC. Suitable for students in Grades 6-8.

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