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# Right triangle altitude theorem

## Description

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean of the two segments equals the altitude. Right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle). 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 opposite side of the triangle). This line containing the opposite side is called the extended base of the altitude. The intersection between the extended base and the altitude is called the foot of the altitude. The shortest altitude (the one from the vertex with the biggest angle) is the geometric mean of the line segments it divides the opposite (longest) side into.

Related formulas

## Variables

 f The altitude from the vertex with the right angle (m) p The one segment on the hypotenuse (m) q The other segment on the hypotenuse (m)