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 exist within the same plane. So, the plane is needed in their definition. Perpendicular lines intersect at a point. Thus, the point is required in their definition.

Answer:

Parallel lines are in the same plane, so plane is needed. Perpendicular lines intersect at a point, so point is needed.