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?

Question

Revolt · Accepted Answer

Parallel lines do not intersect. Parallel lines must be coplanar. Perpendicular lines intersect at one point. Perpendicular lines intersect so plane is not required in the definition.

Defining Terms

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?

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