# Similarity in Right Triangles

In Glogpedia

Last updated 5 years ago

Discipline:
Math
Subject:
Geometry
8,9,10,11,12   Similarity in Right Triangles

By Paul Valdivia

Altitude of a triangle- A perpendicular segment from a vertex to the line containing the opposite side.

Leg of a right triangle- One of the two sides of the right triangle that form the right triangle.

The Geometric Mean- The positive square root of their product. So the geometric mean of a and b is the positive number x such that x=√ab

Theorem 8-1-1The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle. ∆ABC~∆ACD~∆CBD

Example of Geometric Mean:Geometric Mean 4 and 9x=√(4)(9)=36x=6

Leg Theorem: The length of a leg in a right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse adjacent to that leg.

Altitude Theorem: The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse.