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 requires the terms line and plane because line and plane that are parallel cannot cross each other therefore they will never make a point of intersection. The characteristics of that parallel lines consists of lines and planes. Perpendicular lines requires the terms line and point because whenever two lines intersect, it creates a point and whenever two planes intersect, it creates a line. The characteristics of that perpendicular lines are points and lines.

oeerivona oeerivona · Answer 2 · 2021-12-19T17:29:41+01:00

The characteristics of the geometric figures that create the different requirements are;

Parallel lines are lines on the same plane and that are equidistant from each other

Perpendicular lines are lines that form a 90 degree angle at the point of their intersection.

Reasons:

The characteristics of parallel lines are;

The shortest distance between the lines that are parallel is the same at all points along the lines.

The lines are on the same plane.

As the plane is extended indefinitely, the lines do not intersect.

The characteristics of perpendicular lines are;

Perpendicular lines are lines that intersect at a point.

Where two lines are perpendicular, the slope of one line is the negative reciprocal of the other, such that the product of the slopes of two lines that are perpendicular is -1.

The angle formed at the intersection of perpendicular lines is 90°.

An horizontal and a vertical line on the same plane are perpendicular to each other.

Therefore, the characteristics of the geometric figures that create the different requirements are;

Parallel lines are lines on the same plane.

Perpendicular lines are lines that form a 90 degree angle at the point of their intersection.

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