Therefore, the geometric mean of 12 and 2.4 is 18 and 1.5 62/87,21 By the definition, the geometric mean x of any two numbers a and b is given by Therefore, the geometric mean of 18 and 1.5 is Write a similarity statement identifying the three similar triangles in the figure. 62/87,21

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8.1 Geometric Mean.notebook January 22, 2014 Big Idea #2 The leg of the overall right triangle is the geometric mean between the overall hypotenuse and the portion of the hypotenuse adjacent to that leg. C B D A C D x y x y If CD is the altitude (going from the right angle to the hypotenuse) of the overall triangle, then c b a b a

Chapter 8 7 Glencoe Geometry 8-1 Skills Practice Geometric Mean Find the geometric mean between each pair of numbers. 1. 2 and 8 2. 9 and 36 3. 4 and 7 4. 5 and 10 5. 28 and 14 6. 7 and 36 Write a similarity statement identifying the three similar triangles in the figure. 7. …

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Practice B Similarity in Right Triangles Write a similarity statement comparing the three triangles in each diagram. Find the geometric mean of each pair Of numbers. If necessary, give the answer in simplest radical form. 3 and 75 10 and 14 6. 4 and 18 9. 4 and 12.25 12. 15. 4. — and 4 7. tar,d9 Find x, y, and z. 5. 8. 14. 16.

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The geometric mean between 12 and 3 is 6. b. 8 and 4 x = √ab Definition of geometric mean = √8 . 4 a = 8 and b = 4 = √( 2 . 4) . 4 Factor. = √16 . 2 Associative Property = 4 √2 Simplify. The geometric mean between 8 and 4 is 4 √2 or about 5.7. Exercises Find the geometric mean between each pair of numbers. 1. 4 and 4 2. 4 and 6

8-1 Study Guide and Intervention Geometric Mean Geometric Mean The geometric mean between two numbers is the positive square root of their product. For two positive numbers a and b, the geometric mean of a and b is the positive number x in the proportion