1. 6.1 Ratios, Proportions, and the Geometric Mean
Before: You solved problems by writing and solving equations
Now: You will solve problems by writing and solving proportions
Why?: Estimate populations, Doubling cookie recipes, creating blueprints

2. RATIO Ratio – a comparison of two numbers by division
Can be written as:
x to y x : y

3. RATIOS Ratios should be written in simplest form Can compare 3 numbers
4 to 2, or 4:2 must be reduced to 2:1
Is 3:18 in simplest form?
Can compare 3 numbers
3 sides of a triangle a:b:c
Units must be the same

4. EXAMPLE Left handed: Right Handed Right Handed: Left Handed
Have a pet: Don’t have a pet

5. EXAMPLES
In the 2002 Major League baseball season, Sammy Sosa hit 49 home runs and was at bat 556 times. Find the ratio of home runs to the number of times he was at bat.
There are 182 girls in the sophomore class of 305. Find the ratio of girls to total students.
The length of a rectangle is 8 in and its width is 5 in. Find the ratio of length to width.

6. Simplify Ratios Examples - Simplify the ratio
1 ft: 3 yards yard=3 ft
3 L: 10 mL mL=1 L
3 in: 4 ft in=1 ft
24 yards : 3 yards
60 mL : 6 L
15 in : 2 ft

7. Compare ratios of angles in a triangle
The measures in the triangle are in the extended ratio of 1:2:3. Find the measure of the angles.
Step 1:Sketch the triangle and label the angles with the extended ratio.
x+2x+3x=180 Triangle Sum Theorem
6x=180 Combine like terms
x=30 Divide each side by 6
Angle Measures are 30, 60, and 90

8. Your turn
The measures in the triangle are in the extended ratio of 2:4:2. Find the measure of the angles.

9. Proportion – An equation stating that two ratios are equal
PROPORTIONS
Proportion – An equation stating that two ratios are equal
What are the extremes and means of the following ratio?

10. Investigating Geometry Activity 6.1
Work in partnerships
Notify me if your partner is not working and therefore should not receive credit
Answer all questions!

11. Cross Products

12. PROPORTIONS How do you prove two ratios equal a proportion?
Cross – Products!
Do the following ratios form a proportion?

13. Do the following ratios form a proportion?
PROPORTIONS
Do the following ratios form a proportion?
Check

14. What if one of the numbers is missing?
PROPORTIONS
What if one of the numbers is missing?

15. Geometric Mean
Geometric Mean: If given two positive numbers (a and b) it is the x in the equation below.

16. Geometric mean Find the geometric mean of the two numbers 12 and 27

17. Your turn Find the geometric mean of the two numbers. 4 and 25

18. HOMEWORK
Pg 360 #3-4, 7-8, odd, 20-21, odd