Geometric Mean and Right Triangles

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Presentation transcript:

Geometric Mean and Right Triangles

Mean (Arithmetic mean) – Average What is the mean of: 3, 4, 7, 5, 8 & 12?

Median – the middle number of a list when the numbers are arranged in order from smallest to largest. If there are two middle numbers, you must take the mean of those two middle numbers. What is the median of: 4, 13, 5, 7, 12, 13, 9? What is the median of: 5, 6, 9, 12, 15, 32, 15, 16?

Mode – the number or numbers that occur most in a set of data? What is the mode of: 5, 6, 9, 12, 15, 32, 15, 16?

What is the geometric mean of: 9 and 25? Geometric Mean (found between two numbers) -the geometric mean between a and b is the positive number x such that a/x = x/b. What is the geometric mean of: 9 and 25? What is the geometric mean of: 16 and 32? What is the geometric mean of: 4 and 18?

Similarity Theorems: ABC ~ DBA ~ DAC The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other. A B C D ABC ~ DBA ~ DAC

Similarity Theorems: The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse. A B C D

Similarity Theorems: The altitude to the hypotenuse of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse. A B C D