Using the diagram below, describe the relationship as parallel, intersecting, or skew. a) AB and BC b) AE and BF c) EF and AD d) Plane ABC and plane ABF e) Plane AED and plane BFC

Steps to Solve

1. Identify relationships between line segments Examine the given line segments to see how they relate to each other based on their positions in the three-dimensional space formed by the polygon.

2. Analyze segments AB and BC

• Segment $AB$ connects points $A$ and $B$, and segment $BC$ connects points $B$ and $C$.
• Since they share a common point $B$ and lie in the same plane, they are intersecting at point $B$.

3. Analyze segments AE and BF

• Segment $AE$ connects points $A$ and $E$, while segment $BF$ connects points $B$ and $F$.
• Both segments lie in different planes and do not intersect; therefore, they are skew segments.

4. Analyze segments EF and AD

• Segment $EF$ connects points $E$ and $F$, and segment $AD$ connects points $A$ and $D$.
• Both segments are in different planes and do not intersect, leading us to classify them as skew.

5. Analyze planes ABC and ABF

• Plane $ABC$ is formed by points $A$, $B$, and $C$, while plane $ABF$ is formed by points $A$, $B$, and $F$.
• These planes share line segment $AB$ and intersect along it, meaning they are intersecting.

6. Analyze planes AED and BFC

• Plane $AED$ is formed by points $A$, $E$, and $D$, while plane $BFC$ is formed by points $B$, $F$, and $C$.
• These two planes also do not share a common line and do not intersect, so we categorize them as skew.