Altitude (triangle)

In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. forming a right angle with) the opposite side or an extension of the opposite side. The intersection between the (extended) side and the altitude is called the foot of the altitude. This opposite side is called the base of the altitude. The length of the altitude is the distance between the base and the vertex.

The three altitudes intersect in a single point, called the orthocenter of the triangle. If the feet of the altitudes do not all fall on the triangle, then the orthocenter falls outside the triangle.

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.