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Honors Geometry Section 8.2 A Ratios and Proportions.

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Presentation on theme: "Honors Geometry Section 8.2 A Ratios and Proportions."— Presentation transcript:

1 Honors Geometry Section 8.2 A Ratios and Proportions

2 A ratio is a comparison of two numbers by division. Ratios can be written in two ways, as a fraction or using a colon.

3 You are required to simplify all ratios and you may not have a decimal or a fraction as one of the terms in a ratio.

4 Examples: number of boys in class today _____number of girls in class today _____Write a ratio of: a) boys to girls b) girls to boys c) boys to students

5 In addition to the conversions for length in the previous unit, you must know the following weight and volume conversions. 1 ton (T) = __________ pounds (lb) 1 gallon (gal) = __________ quarts (qt) 1 pound (lb) = __________ ounces (oz) 1 quart (qt) = __________ pints (pt) 1 pint (pt) = __________ cups (c)

6 If the two terms in the ratio do not have the same units, you must convert both terms to like units before simplifying.

7 Examples: Simplify. a) b) c) d)

8 and are supplementary. If, what is the ratio of to ?

9 Two complementary angles are in the ratio of 7:13. Find the measure of each.

10 The measures of the angles of a triangle are in the ratio 8:5:3. Find the measures of the angles of the triangle. A ratio with more than two terms is called an ratio. extended

11 A proportion is an equation relating two ratios.

12 If two ratios and are equal, we could write or.

13 The following property makes proportion problems very easy to solve. Cross-Multiplication Property If, then

14 Examples: Solve for x

15 As you can see from examples 1, 4 and 5 above, the terms of a proportion can be rearranged, or even changed, and the resulting proportion will be equivalent to the original proportion as long as the cross-products remain equivalent.

16 Example: Which of the following proportions are equivalent to ?

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