height

Let $A B C$ be a given triangle. A height of $A B C$ is a line segment drawn from a vertex to the opposite side (or its prolongations) and perpendicular to it. So we have three heights in any triangle. The three heights are always concurrent and the common point is called the orthocenter. In Euclidean geometry the length of the segment ”height” is sometimes referred to as the height.

In the following figure, $A D, B E$ and $C F$ are heights of $A B C$ .

Title	height
Canonical name	Height
Date of creation	2013-03-22 11:55:39
Last modified on	2013-03-22 11:55:39
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	15
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 51-00
Related topic	Triangle
Related topic	Median
Related topic	Orthocenter
Related topic	Cevian
Related topic	BaseAndHeightOfTriangle