2. Altitude of a triangle

Altitude of a triangle

An altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).

In ∆ ABC, AD is the altitude of triangle ABC.
Through each vertex, an altitude can be drawn. So, there are at most three altitudes in a triangle.
Properties of Altitudes of a Triangle

• Every triangle has 3 altitudes, one from each vertex. AE, BF and CD are the 3 altitudes of the triangle ABC.
• The altitude is the shortest distance from the vertex to its opposite side.
• The 3 altitudes always meet at a single point, no matter what the shape of the triangle is.
• The point where the 3 altitudes meet is called the ortho-centre of the triangle. Point O is the ortho-centre of the triangle ABC.
• The altitude of a triangle may lie inside or outside the triangle.