6.1 Ratios, Proportions, and the Geometric Mean

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Presentation transcript:

6.1 Ratios, Proportions, and the Geometric Mean Goal: You will solve problems by writing and solving proportions.

Solving Proportions a:b If a and b are two numbers or quantities, and b ≠ 0, then the ratio of a to b is ________ A ratio can also be written as ______________ We want to express ratios in their simplest form (lowest terms). a:b 14 7 2 1

Simplify ratios Example 1: Simplify the ratio. a. 76 cm : 8 cm b. c. 3 yd : 36 ft d.

Use a ratio to find a Dimension Example 2: The perimeter of a rectangular table is 21 feet and the ratio of its length to its width is 5:2. Find the length and width of the table.

Use extended ratios Example 3: The measures of the angles in ∆ BCD are in the extended ratio of 2:3:4. Find the measures of the angles.

On Your Own 3: The measures of the angles in ∆ BCD are in the extended ratio of 1:4:5. Find the measures of the angles.

ad bc a, d  are the extremes (first and last written) b, c  are the means

Why does Cross-Multiplication Work?

Another way…

Proportions Example 4: Solve the proportion. a. b. c. Change on notes

Example 5: 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.

Find the geometric mean between 16 and 48. ab ab Example 6: Find the geometric mean between 16 and 48.

Geometric Mean of 3 and 10 On Your Own 6: Find the altitude of the triangle shown below.