Editing Orthocenter (section)

{{short description|Intersection of triangle altitudes}}
{{distinguish|Orthocenter (tetrahedron)}}
[[File:Triangle.Orthocenter.svg|right|thumb|The three altitudes of a triangle intersect at the orthocenter, which for an [[Acute and obtuse triangles|acute triangle]] is inside the triangle.]]

The '''orthocenter''' of a [[triangle]], usually denoted by {{mvar|H}}, is the [[point (geometry)|point]] where the three (possibly extended) [[altitude (triangle)|altitudes]] intersect.<ref>{{harvnb|Smart|1998|loc = p. 156}}</ref><ref name=BG118>{{harvnb|Berele|Goldman|2001|loc=p. 118}}</ref>  The orthocenter lies inside the triangle [[if and only if]] the triangle is [[acute triangle|acute]]. For a [[right triangle]], the orthocenter coincides with the [[vertex (geometry)|vertex]] at the right angle.<ref name=BG118 /> For an [[equilateral triangle]], all [[triangle center|triangle centers]] (including the orthocenter) coincide at its [[centroid]].