In an isosceles triangle (a triangle with two equal sides), the altitude having as base the third side will have the midpoint of that side as foot.
Altitudes can be used to compute the area of a triangle: it is given by one half of the product of length of altitude and its base.
In a right triangle, the altitude with the hypotenuse as base divides the hypotenuse into two lengths p and q. If we denote the length of the altitude by h, we then have the relation
The orthocenter, along with the centroid, circumcenter and center of the nine point circle all lie on a single line, known as Euler's line. The center of the nine point circle lies at the midpoint between the orthocenter and the circumcenter, and the distance between the centroid and the circumcenter is half that between the centroid and the orthocenter.
Four points in the plane such that one of them is the orthocenter of the triangle formed by the other three are called an orthocentric system.