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Geometry

Geometry. 8.1 Right Triangles. A radical is in simplest form when:. No perfect square factor other than 1 is under the radical sign. No fraction is under the radical sign. No radical is in a denominator. Simplify:. Answers:. Geometric Mean. If a, b and x are positive numbers and.

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Geometry

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  1. Geometry 8.1 Right Triangles

  2. A radical is in simplest form when: • No perfect square factor other than 1 is under the radical sign. • No fraction is under the radical sign. • No radical is in a denominator. Simplify: Answers:

  3. Geometric Mean If a, b and x are positive numbers and mean mean then x is called the geometric mean between a and b. Multiplying means/extremes we find that: Taking the square root of each side: A positive number

  4. Geometric Mean • Basically, to find the geometric mean of 2 numbers, multiply them and take the square root. • Note that the geometric mean always falls between the 2 numbers. Ex: Find the geometric mean between 5 and 11. Use the formula

  5. Geometric Mean Ex: Find the geometric mean between the two numbers. a. 5 and 20 Avoid multiplying large numbers together. Break numbers into perfect square factors to simplify. b. 24 and 32

  6. Geometric Mean Find the geometric mean between the two numbers. • 5 and 20 • 64 and 49 • 1 and 3 • 100 and 6 • 20 and 24

  7. ∆ Review Hypotenuse the side opposite the right angle in a right triangle • Altitude the perpendicular segment from a vertex to the line containing the opposite side

  8. Theorem If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. ~ a a ~ b b

  9. Corollaries When the altitude is drawn to the hypotenuse of a right triangle: Y the length of the altitude is the geometric mean between the segments of the hypotenuse. X A Z Each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse that is adjacent to that leg.

  10. Corollary 1 piece of hypotenuse altitude altitude other piece of hypotenuse = Y X A Z

  11. Corollary 2 hypotenuse leg leg piece of hyp. adj. to leg = Y X A Z

  12. Corollary 2 hypotenuse leg leg piece of hyp. adj. to leg = Y X A Z

  13. C Exercises 8 A x N 16 B 12. If CN = 8 and NB = 16, find AN. Let x = AN

  14. C Exercises x A N B 8 12 14. If AN = 8 and NB = 12, find CN. Let x = CN

  15. C Exercises 12 x A N B 18 17. If AB = 18 and CB = 12, find NB. Let x = NB

  16. Answers Exercises 13 - 19 • 36 • 20 • 2√15 • 25 • 5

  17. Homework pg. 288 #16-30, 31-39 odd

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