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

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Presentation transcript:

Geometry Section 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 and and 18

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