# Perpendicular

## Origin

Middle English *perpendiculer*, from Middle French, from Latin *perpendicularis*, from *perpendiculum* plumb line, from *per*- + *pendēre* to hang

## Definitions

- 1a : standing at right angles to the plane of the horizon : exactly upright

- b : being at right angles to a given line or plane

- 2: extremely steep : precipitous
- 3often capitalized : of or relating to a medieval English Gothic style of architecture in which vertical lines predominate
- 4: relating to, uniting, or consisting of individuals of dissimilar type or on different levels

## Description

In geometry, the word perpendicular describes the relationship between two geometric objects that meet at a right angle.

A line is said to be *perpendicular* to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if 1) the two lines meet and 2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles. Perpendicularity can be shown to be symmetric, meaning if a first line is perpendicular to a second line, then the second line is also perpendicular to the first. For this reason, we may speak of two lines as being perpendicular (to each other) without specifying an order.[1]