Question

contrasting parallel and perpendicular lines
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?
parallel lines are considered in the context of a plane as they exist within the same flat surface and do not meet. perpendicular lines are defined by their intersection at a right angle which is determined by the point where they cross.
sample response: parallel lines never intersect, but they must be in the same plane. the definition does not require the undefined term point, but it does require plane. because they intersect, perpendicular lines must be coplanar; consequently, plane is not required in the definition.
what did you include in your response? check all that apply.
□ 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.

Explanation:

Parallel lines are non - intersecting and coplanar, while perpendicular lines intersect at a single point (at a right - angle). The sample response highlights these key characteristics and the role of the undefined terms in their definitions.

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.