Perpendicular

In geometry, two lines or planes (or a line and a plane) are considered perpendicular (or orthogonal) to each other if they form congruent adjacent angles (a T-shape). The term may be used as a noun or adjective. Thus, as illustrated, the line AB is the perpendicular to CD through the point B.

By definition, a line is infinitely long, and strictly speaking AB and CD in this example represent line segments of two infinitely long lines. Hence the line segment AB does not have to intersect line segment CD to be considered perpendicular lines, because if the line segments are extended out to infinity, they would still form congruent adjacent angles.

If a line is perpendicular to another as shown, all of the angles created by their intersection are called right angles (right angles measure π/2 radians, or 90°). Conversely, any lines that meet to form right angles are perpendicular.

In a coordinate plane, perpendicular lines have opposite reciprocal slopes, which means that the product of their slopes is -1. A horizontal line has slope equal to zero while the slope of a vertical line is described as undefined or sometimes ±infinity. Two lines that are perpendicular would be denoted as ABCD.

Read more about Perpendicular:  Construction of The Perpendicular, In Relationship To Parallel Lines, Perpendicular Symbol, Graph of Functions

Other articles related to "perpendicular":

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... functions y1 = a1x + b1 and y2 = a2x + b2, the graph of the functions will be perpendicular and will make four right angles where the lines intersect if and only if a1a2 = −1 ... The lines will be perpendicular if and only if a1a2 + b1b2 = 0 ...
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... The Perpendicular Gothic east window of the chancel was added in the second half of the 14th century ... One of the aisles was also rebuilt in Perpendicular Gothic, and the bell tower was added late in the Perpendicular period (15th or early 16th century) ... There are two carved wooden screens a Perpendicular one to the north chapel and a very well-carved Jacobean one to the tower ...
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