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Geometry Section 6.1 Ratios, Proportions, and the Geometric Mean.

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Presentation on theme: "Geometry Section 6.1 Ratios, Proportions, and the Geometric Mean."— Presentation transcript:

1 Geometry Section 6.1 Ratios, Proportions, and the Geometric Mean

2 Ratio The ratio of a to b is Also written as a:b Usually expressed in simplest form 2 ratios that have the same simplified forms are called equivalent ratios

3 Examples Simplify the ratio 24 yards to 3 yards 150 cm : 6 m 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.

4 Using extended ratios A triangle’s angle measures are in the extended ratio of 1 : 3 : 5. find the measures of the angles.

5 Proportions An equation that states that the two ratios are equal. Cross product property. In a proportion the product of the extremes equals the product of the means.

6 Examples Solve the Proportion

7 Example 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.

8 Geometric Mean The geometric mean of two positive numbers a and b is the positive number x that satisfies so and

9 Examples Find the geometric mean of the two numbers 12 and 27 18 and 54 16 and 18

10 Assignment Section 6.1 Page 360 Problems #4 – 44 even, 50


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