Altitude

### 1. An altitude of a triangle

1. An altitude is a line which passes through a vertex of a triangle, and meets the opposite side at right angles. A triangle has three altitudes. For more see Altitudes of a triangle.

An interesting fact is that the three altitudes always pass through a common point called the orthocenter of the triangle. See Orthocenter of a triangle

2. The length of a perpendicular from a side of the triangle to the opposite vertex. This is often used to calculate the area of a triangle. See Area of a triangle.

### 2. Quadrilaterals with a pair of parallel sides

If a quadrilateral has a pair of parallel sides, both of them are called a base. In a similar way to triangles, the altitude of such a figure is the perpendicular distance from a base to the opposite side. Since they are parallel, either one will do.

Note: A common mistake is to use the length of the slanted side as the altitude. This is wrong. You must use the vertical distance as shown.

## Pages referring to 'altitude'

The altitude of a triangle is the perpendicular from a vertex to the opposite side.
The conventional method of calculating the area of a triangle (half base times altitude) with pointers to other methods and special formula for equilateral triangles
This page shows how to construct one of the three altitudes of a triangle, using only a compass and straightedge or ruler. A Euclidean construction.
This page shows how to construct one of the three altitudes of an obtuse triangle, using only a compass and straightedge or ruler. A Euclidean construction.
Definiton and properties of a trapezoid (coordinate geometry) including altitude and median
Definition and properties of triangles