Question

the definition of parallel lines requires the undefined terms line and plane, while the definition of perpendicular lines requires the undefined terms of line and point. what characteristics of these geometric figures create the different requirements?

Explanation:

Parallel lines are in the same plane and never intersect, so the concept of a plane is needed to define their non - intersection in a flat surface. Perpendicular lines are defined by the right - angle formed at their intersection point. So, a point is required to mark the location of intersection.

Answer:

Parallel lines need the concept of a plane to define non - intersection in a flat surface, while perpendicular lines need a point to mark the intersection location.