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NAME: ______________________________ DATE: _____________ PERIOD: ______ Geometry Notes Ratio, Proportion, & Geometric Mean If a and b are two quantities that are measured in the _________ units, then the ratio of a to b is written as: OR Examples: Simplify the ratios. 1)8 books = 12 books 2) 24 trees= 14 tress 3) 18 balls= 36 balls 4) 48 feet= 36 feet Answer these questions: The girls soccer team won 10 games and lost 2, the boys soccer team won 12 games lost 3. A) What is the ratio of girl’s wins to their losses. B) What is the ratio of boy’s wins to their losses. C) What is the ratio of girl’s wins to the total number of games played? D) What is the ratio of boy’s wins to the total number of games played? E) Which team had the better record? Use a number line to find the ratio of the distances. AB DE BC DE AC BD CF AB Find the ratio of width to length of the rectangles. Remember to simplify. Solving word problems. 1) The measures of the angles in a triangle are in an extended ratio of 3: 4: 5. Find the measures of the angles. 2) The area of a rectangle is 192 sq. feet. The ratio of the width to the length is 3 : 4. Find the width and the length. The ratio of the given side lengths of the triangle is given. Solve for the variable. 3) AB : BC is 2: 5 4) AC:BC:AB is 2 : 1: 2 NAME: ______________________________ DATE: _____________ PERIOD: ______ Geometry Notes- Section 6.1-PAGE 2 Ratio & Proportion An equation that equates two ratios is called a ___________________. To solve proportions we use the Cross Product Property: The product of the means is equal to the product of the extremes. a c b d where ad = bc a & d are: ____________ b & c are: ______________ Solve these proportions. 1) 4) 20 m 30 120 2 3 y 3 y 2) 5) y 2 10 5 3 15 d 2 d 3) 6) 5 x 10 16 5 3 2n 7 n 3 Geometric Mean: The geometric mean of two positive numbers a and b is the positive number x such that a x = x b To solve: Examples: Find the geometric mean. 1) 4 and 9 4) 16 and 18 2) 4 and 16 3) 3 and 12 5) 18 and 54