–Ratios,Proportions,andtheGeometricMean61–比例比例和几何平均.ppt

1、6.1 Ratios, Proportions, and the Geometric Mean,If a and b are two numbers or quantities and b does not equal zero, 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 of Triangle ABC to a side length in Triangle DEF can be written

2、 as 2/1 or 2:1.,6.1 Ratios, Proportions, and the Geometric Mean,Example 1: Simplify the ratio. a. 64 m: 6 mb. 5 ft / 20 in,6.1 Ratios, Proportions, and the Geometric Mean,Example 1: Simplify the ratio. c. 24 yds to 3 ydsd. 150 cm: 6 m,6.1 Ratios, Proportions, and the Geometric Mean,Example 2: You ar

3、e planning to paint a mural on a rectangular wall. You know that the perimeter of the wall is 484 feet and that the ratio of its length to its width is 9:2. Find the area of the wall.,6.1 Ratios, Proportions, and the Geometric Mean,Example 3: The measures of the angles in Triangle CDE are in the ext

4、ended ratio of 1:2:3. Find the measures of the angles.,6.1 Ratios, Proportions, and the Geometric Mean,Example 4: The perimeter of a room is 48 feet and the ratio of its length to its width is 7:5. Find the length and width of the room.,6.1 Ratios, Proportions, and the Geometric Mean,Example 5: The

5、measures of the angles in Triangle CDE are in the extended ratio of 1:3:5. Find the measures of the angles.,6.1 Ratios, Proportions, and the Geometric Mean,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

6、 d are the extremes of the proportion.,6.1 Ratios, Proportions, and the Geometric Mean,6.1 Ratios, Proportions, and the Geometric Mean,Example 6: Solve the proportion.,6.1 Ratios, Proportions, and the Geometric Mean,Example 7: Solve the proportion. As part of an environmental study, you need to estimate the number of trees in a 150 acre area. You count 270 trees in a 2 acre area and you notice that the trees seem to be evenly distributed. Estimate the total number of trees.,6.1 Ratios, Proportions, and the Geometric Mean,6.1 Ratios, Proportions, an