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Similarity in Right Triangles. 7-4. Warmup activity (don’t need to turn in). Complete activity on p. 391 with a partner. Theorem. In a right triangle, the altitude to the hypotenuse yields three similar triangles. B. A. C. D. Example. b. a. e. c. d. f. b. f. a. a. e. d. c.
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Warmup activity (don’t need to turn in) Complete activity on p. 391 with a partner
Theorem In a right triangle, the altitude to the hypotenuse yields three similar triangles. B A C D
Example b a e c d f b f a a e d c e b
Geometric Mean Proportions in which the means are equal occur frequently in geometry. For any two positive numbers a and b, the geometric mean of a and b is the positive number such that Note that
Examples – Finding the geometric mean Find the geometric mean of the following numbers (round to two decimal places): a. 4 and 18 b. 15 and 20 c. 3 and 12
Corollary 1 The lengths of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the segments of the hypotenuse.
Examples Find the missing variables: 50 6 x 40 x 4
Corollary 2 When the altitude to the hypotenuse of a right triangle separates the hypotenuse, the length of each leg is the geometric mean of the length of the adjacent hypotenuse segment and the length of the hypotenuse.
Applying Corollaries 1 and 2 Solve for x and y and z. You try z x y 4 12 4 5 x y z
Hwk • P. 394-395: 1-20, 34-36,49-51