Honors Geometry Section 8.2 A Ratios and Proportions

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.

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.

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

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)

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

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

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

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.

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

A proportion is an equation relating two ratios.

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

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

Examples: Solve for x. 1. 2. 3. 4. 5.

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.

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