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.

*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.

The three altitudes all intersect at the same point so we only need two to locate it. The proof for the third one is similar to the above.

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.