Chapter 8.1 GM

Lesson 8-1:

Lesson 7-1: Geometric Mean 1 Geometric Mean Lesson 8-1

The Geometric Mean of two numbers = the Square Root of the Product of the two numbers:

Lesson 7-1: Geometric Mean 2 The Geometric Mean of two numbers = the Square Root of the Product of the two numbers To find the geometric mean between 7 and 28 ... 7 , ___ , 28 label the missing term x write a proportion cross multiply solve

The geometric mean between two numbers a and b is the positive number x where . Therefore x = .:

Lesson 7-1: Geometric Mean 3 The geometric mean between two numbers a and b is the positive number x where . Therefore x = . Try It: Find the geometric mean of . . . 1. 10 and 40 Answer = 20 2. 1 and 36 Answer = 6 3. 10 and 20 Answer = 14.14 4. 5 and 6 Answer = 5.48 5. 8.1 and 12.2 Answer = 9.94

How does this relate to geometry?:

Lesson 7-1: Geometric Mean 4 How does this relate to geometry?

Slide 5:

Lesson 7-1: Geometric Mean 5 The " W " Pattern

The Geometric Means:

Lesson 7-1: Geometric Mean 6 The Geometric Means Recall the three geometric means that you discovered from your Sketchpad activity. BUT FIRST . . .

Re-label the Sides (as lengths):

Lesson 7-1: Geometric Mean 7 Re-label the Sides (as lengths)

Geometric Mean #1:

Lesson 7-1: Geometric Mean 8 Geometric Mean #1 f is the geometric mean of d and e. What is the proportion that uses f?

Geometric Mean #2:

Lesson 7-1: Geometric Mean 9 Geometric Mean #2 b is the geometric mean of e and c. What is the proportion that uses b?

Geometric Mean #3:

Lesson 7-1: Geometric Mean 10 Geometric Mean #3 a is the geometric mean of d and c. What is the proportion that uses a?

Put them all together:

Lesson 7-1: Geometric Mean 11 Put them all together

The “W” Pattern:

Lesson 7-1: Geometric Mean 12 The “W” Pattern W

Try it !:

Lesson 7-1: Geometric Mean 13 Try it ! Given: d = 4 and e = 10 Find: a = ___ b = ___ c = ___ f = ___

Solution::

Lesson 7-1: Geometric Mean 14 Solution: Proportions Answers