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?

The characteristic of these geometric figures that create the different requirements would be how these the undefined terms are situated. For the case of parallel lines, these are lines that would not intersect now matter how long the line is extended or whether it goes infinitely thus the lines lie on the same plane. For perpendicular lines, these lines would intersect at one point and would form angles which measure 90 degrees on that point. Thus, these lines can be situated at any plane as long as they intersect with a 90 degrees angle.