GeometrySection 6.1 Ratios, Proportions, and the Geometric Mean
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
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.
Using extended ratios • A triangle’s angle measures are in the extended ratio of 1 : 3 : 5. find the measures of the angles.
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.
Examples • Solve the Proportion
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.
Geometric Mean • The geometric mean of two positive numbers a and b is the positive number x that satisfies so and
Examples • Find the geometric mean of the two numbers • 12 and 27 • 18 and 54 • 16 and 18
Assignment • Section 6.1 • Page 360 • Problems #4 – 44 even, 50