Geometric Geometric Mean Mean and and Right Right

TrianglesTriangles

Mean (Arithmetic mean) – Mean (Arithmetic mean) – AverageAverage

What is the mean of: 3, 4, 7, 5, 8 & 12?

Median – the middle number Median – the middle number of a list when the numbers of a list when the numbers are arranged in order from are arranged in order from smallest to largest. If there smallest to largest. If there are two middle numbers, you are two middle numbers, you must take the mean of those must take the mean of those two middle numbers.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 Mode – the number or numbers that occur most in numbers that occur most in a set of data?a set of data?

What is the mode of:

5, 6, 9, 12, 15, 32, 15, 16?

Geometric MeanGeometric Mean (found between two (found between two numbers) numbers) -the geometric mean -the geometric mean between a and b is the between a and b is the positive number x such that positive number x such that aa//xx = = xx//bb..

What is the geometric mean of: 4 and 18? What is the geometric mean of: 9 and 25? What is the geometric mean of: 16 and 32?

Similarity Theorems:Similarity Theorems:

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 CD

ABC ~ DBA ~ DAC

Similarity Theorems: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 CD

Similarity Theorems: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 CD