# Similarity in Right Triangles

by
**Chessphysics**

Last updated 6 years ago

** Discipline: **

Math ** Subject: **

Geometry
** Grade:**

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.

Test Yourself!Scroll down to check your work:Answer:a² =DB(AB)x² =2(8)x² =16√x² =√16x=4

Test Yourself!Scroll down to check your work:Answer:8² =AD(DB)8²=4x64=4x4 416=x

Definitions:

Theorems:

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