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The concept of the geometric mean between two numbers and its application in right triangles. It also derives the relationship between the sides of a right triangle when an altitude is drawn to the hypotenuse, leading to the similarity of the formed triangles. Examples and a theorem.
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What are the terms x and y in the proportion shown called? If a , b , and x are positive numbers and then x is called the geometric mean between a and b. Geometric mean - the result when you multiply two numbers and take the square root. What is the geometric mean?
Examples: Find the geometric mean between the following:
Identify the three triangles: Small - Medium - Large - Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. List all proportions for each pair of similar triangles.
