1. 8.1: Ratios and Proportions
GEOMETRY: Chapter 8
8.1: Ratios and Proportions

2. If a and b are two numbers or quantities and b≠0, then the ratio of a to b is a/b. The ratio of a to b can also be written as a:b.
For example, the ratio of a side length in triangle DEF to a side length in ABC can be written as ½ or 1:2.
Image taken from: Geometry. McDougal Littell: Boston, P. 356.

3. Ex. 1: Simplify the ratio. 12km: 3km 36 in.; 9ft 100cm:2m 3 ft: 30 in.
Answers:
4:1
b. 1:3
c. 1:2
d. 6:5

4. Ex. 2:
The area of a rectangular garden is 108 square feet, and the ratio of the length to the width is 4:3.
Find the length and width of fence needed to enclose the garden.
Answer: length—12 feet, width—9feet

5. Ex. 3.
The measure of the angles of triangle RST are in the extended ratio 2:3:4. Find the measures of the angles.
Answers: 400, 600, 800
Image taken from: Geometry. McDougal Littell: Boston, P. 358.

6. Proportions: An equation that states that two ratios are equal is called a proportion.
The numbers b and c are the means of the proportion. The numbers a and d are the extremes of the proportion.
Image taken from: Geometry. McDougal Littell: Boston, P. 358.

7. A Key Property of Proportions
Cross Products Property: In a proportion, the product of the extremes equals the product of the means.
Reciprocal Property—If two ratios are equal, then their reciprocals are also equal.
Image taken from: Geometry. McDougal Littell: Boston, P. 358.

8. Ex.4
Solve the proportion.

9. Ex.4
Solve the proportion.
Answer: a. 9; b. 5

10. Ex.5
As part of a science project, you need to estimate the number of blue spruce trees in a 50 acre forest. You count 36 trees in 3 acres and notice that the trees seem to be evenly distributed. Estimate the total number of blue spruce trees in the forest.

11. Ex.5
As part of a science project, you need to estimate the number of blue spruce trees in a 50 acre forest. You count 36 trees in 3 acres and notice that the trees seem to be evenly distributed. Estimate the total number of blue spruce trees in the forest.
Answer: about 600 trees.

12. Geometric Mean
The geometric mean of two positive numbers a and b is the positive number x that satisfies
So, x2=ab and

13. Ex.6
Find the geometric mean of 36 and 54.

14. Ex.6
Find the geometric mean of 36 and 54.
Answer:

15. 6.1, p. 360, #1-25 odds, odds
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