Orthocenter of a Triangle
From Greek: orthos - "straight, true, correct, regular"
Try this Drag the orange dots on any vertex
to reshape the triangle. Notice the location of the orthocenter.
(If there is no image below, see support page.)
The altitude of a triangle is the perpendicular distance from a vertex
of the triangle to the side opposite that vertex. There are therefore three altitudes possible, one from each vertex.
It turns out that all three altitudes always intersect at the same point - the so-called orthocenter of the triangle.
The orthocenter is not always inside the triangle. If the triangle is
obtuse, it will be outside.
To make this happen the altitude lines have to be extended so they cross. Adjust the figure above and create a triangle where the orthocenter is outside the triangle.
Follow each line and convince yourself that the three altitudes, when extended the right way, do in fact intersect at the orthocenter.
Constructing the Orthocenter of a triangle
It is possible to construct the orthocenter of a triangle using a compass and straightedge. See
Constructing the the Orthocenter of a triangle.
Related triangle topics
General
Triangle types
Triangle centers
Congruence and Similarity
Triangle quizzes and exercises
(C) 2007 Copyright John Page
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