Altitudes and orthocentre

An altitude of a triangle is the line that passes through a vertex and is perpendicular to the opposite side. All three altitudes of a triangle intersect at one and the same point, called the orthocentre of the triangle. The point where the altitude intersects the side of a triangle is called the foot of the altitude. The length of the segment on the altitude from the vertex to the foot is called the height of a triangle, and the segment that contains the foot is called the base.

Theorems of altitudes and orthocentre

• The orthocentre is inside an acute triangle, at the vertex of the right angle in a right triangle, and outside an obtuse triangle.