Question

contrasting parallel and perpendicular lin
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 plane is needed. Perpendicular lines are defined by the 90 - degree angle formed at a point of intersection, thus the concept of point is crucial.

Answer:

Parallel lines are related to the plane they lie in as they are non - intersecting within that plane. Perpendicular lines are defined by their intersection at a point with a right - angle relationship.