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Based on the diagram of the rectangular prism, we can classify the segments as parallel, perpendicular, skew, or congruent based on their spatial relationships.

Here are the relationships for the segments:

1. **Segment BC and segment AE**: These two segments are on different faces and not parallel, perpendicular, or intersecting. Hence, they are **skew segments**.
2. **Segment EH and segment DH**: These two segments meet at point H and form a right angle, so they are **perpendicular segments**.
3. **Segment BC and segment FG**: These segments are on opposite parallel faces of the prism, so they are **parallel segments**.
4. **Segment AB and segment CG**: These segments are on different faces and do not intersect or run parallel, meaning they are **skew segments**.

The correct classifications would be:

- **Skew Segments**: BC and AE, AB and CG
- **Perpendicular Segments**: EH and DH
- **Parallel Segments**: BC and FG

Would you like more details on how these relationships are determined? Here are some follow-up questions:

1. What does it mean for two segments to be skew?
2. Can two skew segments ever be congruent?
3. How can we verify if two segments in 3D space are perpendicular?
4. What defines two segments as parallel in three-dimensional geometry?
5. Can a pair of skew segments become parallel if the shape of the figure changes?

**Tip**: When analyzing geometric figures, visualizing or drawing the shape from different perspectives helps clarify the spatial relationships of segments.

Classify the relationships between various line segments in the given rectangular prism, such as BC and AE, EH and DH, BC and FG, and AB and CG.

Explore the classification of segment relationships in a rectangular prism. Learn about skew, parallel, and perpendicular segments through examples like BC and AE (skew), EH and DH (perpendicular), BC and FG (parallel). Suitable for middle school students.

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