Orthocenter of a Triangle
Geometry construction using a compass and straightedge

This page shows how to construct the orthocenter of a triangle with compass and straightedge or ruler. For a more, see orthocenter of a triangle. The orthocenter is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. There are therefore three altitudes in a triangle. It works using the construction for a perpendicular through a point to draw two of the altitudes, thus location the orthocenter.

Geometry construction with compass and straightedge or ruler or ruler *Note  If you find you cannot draw the arcs in steps 2 and 3, the orthocenter lies outside the triangle. See Orthocenter of a triangle.

To solve the problem, extend the opposite side until you can draw the arc across it. (See diagram right). Then proceed as usual.

Printable step-by-step instructions

The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.

Try it yourself

Click here for a printable worksheet containing two triangle orthocenter problems. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Constructions pages on this site




Right triangles

Triangle Centers

Circles, Arcs and Ellipses


Non-Euclidean constructions


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