https://file.aiquickdraw.com/mathbot/file/1727109878638rx0bbaek.jpg

The image shows a geometric problem involving a rectangular prism. You need to determine the relationship between line segments or planes, specifically whether they are parallel, skew, or perpendicular.

Let's analyze the statements one by one:

1. **\(\overline{AB}\) and \(\overline{FB}\) are**:
   - These two line segments are **perpendicular** because \(\overline{AB}\) is vertical, and \(\overline{FB}\) is horizontal.

2. **\(\overline{CD}\) and \(\overline{EF}\) are**:
   - These segments are **parallel** because they are on opposite sides and run in the same direction.

3. **\(\overline{GH}\) and \(\overline{AE}\) are**:
   - These segments are **skew** because they are not parallel and do not intersect, existing in different planes.

4. **Plane \(CDH\) and plane \(ABF\) are**:
   - These planes are **perpendicular** because the vertical side and horizontal base meet at a right angle.

5. **Plane \(GEF\) and plane \(AEG\) are**:
   - These planes are **perpendicular** since one plane is a vertical face, and the other is a horizontal top face of the prism.

Would you like any additional details or explanations? 

Here are some related questions:
1. How can you identify skew lines in a 3D figure?
2. What are the properties of parallel planes?
3. How do perpendicular lines and planes interact in a three-dimensional shape?
4. What is the difference between skew lines and parallel lines?
5. How do you determine the relationships between planes in three-dimensional geometry?

**Tip:** To determine if lines are skew, check if they lie in different planes and do not intersect.

Think of each segment in the diagram as part of a line. Complete the statement with parallel, skew, or perpendicular. The segments and planes involved are \(\overline{AB}\) and \(\overline{FB}\), \(\overline{CD}\) and \(\overline{EF}\), \(\overline{GH}\) and \(\overline{AE}\), plane CDH and plane ABF, plane GEF and plane AEG.

Learn how to identify relationships such as parallel, skew, and perpendicular lines and planes in a 3D rectangular prism. This problem involves analyzing line segments like \(\overline{AB}\), \(\overline{FB}\), \(\overline{CD}\), and \(\overline{EF}\) and planes like CDH and ABF. Suitable for students in Grades 9-12.

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