Geometry

Question Analysis

This question involves the concept of parallel lines in the context of a 3D figure. The main focus is on applying the definition of parallel lines to identify which line is not parallel to the given line.

Key Concept Explanation:

Parallel lines are defined as coplanar lines that do not intersect each other, no matter how far they are extended.

Option Analysis

HG is not parallel to FG. HG and FG share the point G, they intersect. Since parallel lines do not intersect, HG is not parallel to FG.

The other lines are parallel to FG:

AD: AD and FG are in different planes. But in a cube, AD is parallel to BC, and BC is parallel to FG (because BC and FG are opposite sides of the square faces of the cube and are coplanar and do not intersect). So AD is parallel to FG (by the transitive property of parallel lines).