1. Ratios and Proportions
Keystone Geometry

2. Ratio A ratio is a comparison of two numbers such as a : b. Ratio:
When writing a ratio, always express it in simplest form.
** Ratios must be compared using the same units.
A ratio can be expressed: 1. As a fraction
2. As a ratio 3 : 7
3. Using the word “to” 3 to 7

3. Example: What is the ratio of side AB to side CB in the triangle?
3.6 6 8
4.8 10
Now try to reduce the fraction.
Example: What is the ratio of side DB to side CD in the triangle?
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4. Example ……….
A baseball player goes to bat 348 times and gets 107 hits. What is the players batting average?
Solution:
Set up a ratio that compares the number of hits to the number of times he goes to bat.
Ratio:
Convert this fraction to a decimal rounded to three decimal places.
Decimal:
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The baseball player’s batting average is which means he is getting approximately one hit every three times at bat.

5. Proportion
Definition: A proportion is an equation stating that two ratios are equal.
For example,

6. Terms of a Proportion First Term Third Term Second Term Fourth Term
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Third Term
Second Term

7. Means and Extremes
The first and last terms of a proportion are called extremes.
The middle terms are called the means.
** The product of the means is always equal to the product of the extremes.

8. Properties of Proportions
is equal to:
Cross-multiplication
Switching the means
Add one to both sides
Reciprocals

9. Example: If , then… 2x
5y = _____

10. ** Special Note: The easiest way to decide if two proportions are equal is to apply the mean-extremes property (cross multiplication). However, all of the other properties work as well, provided your initial proportion is true.

11. Proportions- examples….
Solve the proportion using cross multiplication.
4 • x =
12 • 3
4x = 36
x = 9
4x = 36

12. Some to try…

13. Example 2: Use a proportion to solve for the missing piece of a triangle.
84 yards
2 ft x
356 yards
Find the value of x.
First! Multiply by 3 to change yards into feet. The units must be the same.
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14. Examples: Find the measure of each angle.
Two complementary angles have measures in the ratio
2 : 3.
Two supplementary angles have measures in the ratio
3 : 7.
The measures of the angles of a triangle are in a ratio of 2 : 2 : 5.
The perimeter of a triangle is 48cm and the lengths of the sides are in a ratio of 3 : 4 : 5. Find the length of each side.
36 and 54
54 and 126
40, 40, and 100
12cm, 16cm, and 20cm