Question

use the figure below to answer questions 1 - 3.

1. name a plane parallel to plane abc.
2. name two segments parallel to segment fb.
3. name two segments skew to segment ab.

Explanation:

1. Plane parallel to plane \(ABC\)

Step1: Recall the property of parallel planes in a rectangular prism

In a rectangular prism (like the given figure), opposite faces (planes) are parallel. Plane \(ABC\) is the bottom - front face. The opposite face (top - back) is plane \(EFG\).

2. Segments parallel to segment \(FB\)

Step1: Identify parallel segments in a rectangular prism

In a rectangular prism, edges that are in the same direction and do not intersect are parallel. Segment \(FB\) is a vertical edge (assuming the standard orientation). Segments \(GC\) and \(HD\) are parallel to \(FB\) (they have the same direction and do not intersect \(FB\)).

3. Segments skew to segment \(AB\)

Step1: Recall the definition of skew lines

Skew lines are non - parallel and non - intersecting lines in 3 - D space. Segment \(AB\) is a horizontal edge on the bottom - front face. Segments \(GC\) and \(EH\) are skew to \(AB\) (they are not in the same plane as \(AB\), and they are neither parallel nor intersecting with \(AB\)).

Answer:

1. Plane \(EFG\)
2. Segments \(GC\) and \(HD\)
3. Segments \(GC\) and \(EH\)