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.