Perpendicular is a geometric term that may be used as a noun or adjective. The fundamental meaning pertains to the position of straight lines relative to one another. Two lines are said to be perpendicular if they meet at a right angle. Note that two line segments positioned at 90° to one another are perpendicular only if they meet. Any two lines in Euclidean space which are perpendicular to one another and which intersect automatically define a plane. Two lines are considered perpendicular if their slopes are negative reciprocals.

Naturally, if a line is given, then a perpendicular is any line at a ninety-degree angle to that line. This is an important property in geometry and trigonometry since important properties accrue to line systems containing right angles. When graphing, the convention is to use either an X and Y axis, or to use an X, Y, and Z axis, which are defined as being mutually perpendicular. Right triangles, too, include two perpendicular lines and so have special properties, which are the foundation of trigonometry.

Compare to parallel.

See also

• orthogonal
• surface normal
• Web Link

Perpendicular is also applied to a late English style of Gothic architecture.