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**Honors Geometry Section 8.2 A Ratios and Proportions**

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**A ratio is a comparison of two numbers by division**

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

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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.

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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

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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)

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

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

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

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**Two complementary angles are in the ratio of 7:13**

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

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**The measures of the angles of a triangle are in the ratio 8:5:3**

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

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**A proportion is an equation relating two ratios.**

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

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**The following property makes proportion problems very easy to solve**

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

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Examples: Solve for x

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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.

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**Example: Which of the following proportions are equivalent to. 1. 2. 3**

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