Let ABC be a given triangle. A height of ABC is a line segmentMathworldPlanetmath drawn from a vertex to the opposite side (or its prolongations) and perpendicularMathworldPlanetmathPlanetmathPlanetmath to it. So we have three heights in any triangle. The three heights are always concurrentMathworldPlanetmath and the common point is called the orthocenterMathworldPlanetmath. In Euclidean geometryMathworldPlanetmath the length of the segment ”height” is sometimes referred to as the height.

In the following figure, AD,BE and CF are heights of ABC.

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