Adjective

perpendicular (comparative more perpendicular, superlative most perpendicular)

1. (geometry) At or forming a right angle (to).

   In most houses, the walls are perpendicular to the floor

Synonyms

• normal
• orthogonal

Noun

perpendicular (plural perpendiculars)

1. (geometry) A line or plane that is perpendicular to another.
2. A device such as a plumb line that is used in making or marking a perpendicular line.

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, referring to Figure 1, the line AB is the perpendicular to CD through the point B. Note that 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 bending to another as in Figure 1, all of the angles created by their intersection are called right angles (right angles measure ½π radians, or 90°). Conversely, any lines that meet to form right angles are perpendicular.

In a coordinate plane, perpendicular lines have opposite reciprocal slopes. 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

Numerical criteria