1. Bellwork – 1/6/15

2. Unit 6: Section 6.1 Ratios, Proportions, and the Geometric Mean (Starts on Page 356)

3. Ratios 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

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

5. Use a ratio to find a Dimension Example 2: The perimeter of a rectangular table is 28 feet and the ratio of its length to its width is 5:2. Find the length and width of the table. 5:2 Length = 5x Width = 2x 2 L + 2 W = p 2 (5x) + 2 (2x) = 28 10x + 4x = 28 14x = 28 x = 2 Length 5x = 5(2) = 10 ft Width 2x = 2(2) = 4 ft

6. 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. 2:3:4 2x:3x:4x Sum of angles = 180 2x + 3x + 4x = 180 9x = 180 X = 20 Angle measurements = 40, 60, 80 degrees

7. Proportion A equation that states that two ratios are equal

8. Cross product property In a proportion, the product of the extremes equals the product of the means If where and, then

9. Proportions Example 4: Solve the proportion. a. b. c. 5 (16) = 10 x 80 = 10 x X = 8 2 ( 8) = 5 (7x) 16 = 35x X = 16/35 3y = 2(y+1) 3y = 2y +2 Y = 2

10. 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. Set up a proportion: 40500 = 2x X = 20250 trees

11. The geometric mean of two positive numbers a and b is the positive number x that satisfies. So, and Geometric Mean

12. Find the Geometric Mean of 12 and 27 Geometric Mean

13. Homework – Geometry Page 360: Exercises: 4, 5, 11, 13, 18 – 30 Even