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? (2023)

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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 will not intersection, while perpendicular lines will intersect at a single point such that the lines are 9 0 o 90^o 90o. Any two lines will always form a plane. Therefore, its the orientation of the lines in relation to the other line which creates the different requirements.

If two non-vertical lines that are in the same plane has the same slope, then they are said to be parallel. Two parallel lines won't ever intersect. If two non-vertical lines in the same plane intersect at a right angle then they are said to be perpendicular.

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 never intersect, but they must be in the same plane.

Answer and Explanation:

The undefined terms needed to define parallel lines are 'lines' and 'points. ' In geometry, there are three undefined terms: points, lines, and planes.

In Mathematics, a perpendicular is defined as a straight line that makes the right angle (90 degrees) with the other line. In other words, if two lines intersect each other at the right angle, then the lines are perpendicular to each other.

Theorem 47: Two parallel lines determine a plane. Postulate 1: If a line intersects a plane not containing it, then the intersection is exactly one point. Postulate 2: If two planes intersect, their intersection is exactly one line.

Vertical lines and horizontal lines are perpendicular to each other. The slope of the perpendicular line in this case would be the slope of a vertical line which would be undefined. The slope of the parallel line is 0 and the slope of the perpendicular line is undefined.

Two lines are either intersecting or parallel. Two lines formed by two perpendicular line segments are also perpendicular. Two segments in a plane are either parallel or perpendicular.

So the three key terms that are not definable, but only describable, are the line, which is a set of points extending infinitely in one or the other direction; plane, which is a flat surface with no thickness; and the third undefined term is point and that has a location and no size.

Undefined Terms. In geometry, point, line, and plane are considered undefined terms because they are only explained using examples and descriptions. Name the points, Lines, & Planes. Collinear points are points. that lie on the same line.

How do you prove a line is parallel or not? ›

To see whether or not two lines are parallel, we must compare their slopes. Two lines are parallel if and only if their slopes are equal. The line 2x – 3y = 4 is in standard form. In general, a line in the form Ax + By = C has a slope of –A/B; therefore, the slope of line q must be –2/–3 = 2/3.

The slopes of parallel lines are equal, and the slopes of perpendicular lines are opposite reciprocals.

Perpendicular lines are those lines that intersect each other at 90 degrees. Do perpendicular lines have to meet? These lines always intersect at right angles.

Key Takeaways. Parallel lines have the same slope. Perpendicular lines have slopes that are opposite reciprocals. In other words, if m=ab, then m⊥=−ba.

A Parallel circuit has certain characteristics and basic rules: A parallel circuit has two or more paths for current to flow through. Voltage is the same across each component of the parallel circuit. The sum of the currents through each path is equal to the total current that flows from the source.