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8.1 Radicals/Geometric Mean

8.1 Radicals/Geometric Mean. Radicals: ____________ _____________________________________ _____________________________________ ____________________________________. Rules for Radicals :. _________________________________ _________________________________ ________________________________.

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8.1 Radicals/Geometric Mean

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  1. 8.1 Radicals/Geometric Mean

  2. Radicals: ____________ • _____________________________________ • _____________________________________ • ____________________________________

  3. Rules for Radicals: • _________________________________ • _________________________________ • ________________________________

  4. Rationalizing: ___________________________ • _______________________________________ • Geometric Mean: ________________________ • _______________________________________ • ____________________________________ • ____________________________________

  5. Find the geometric mean of 9 and 4:

  6. Corollary 1: _________________________ ___________________________________ ___________________________________ ___________________________________ a y x

  7. Corollary 2: _________________________ ___________________________________ ___________________________________ ___________________________________ s1 s2 x y z

  8. Solve for x, y and a: x y a 16 9

  9. 8.2 Pythagorean Theorem

  10. Theorem 8.2: _____________________ ___________________________________ ___________________________________ c a b

  11. Examples: 10 m 5 5 y m-1

  12. 15 13 13 x 25

  13. 8.3 Converse of thePythagorean Theorem

  14. Theorem 8.3: ___________________________ _______________________________________ ___________________________________ ___________________________________ There are a lot of standard families of right triangles. Make your life easier and memorize the head of each family.

  15. 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25 Memorize the Read ones!!

  16. Examples: 13 50 5 14 y x

  17. What happens if it is not a right triangle? • _______________________________________ • ________________________________________ • _______________________________________

  18. Examples: Tell what kind of Triangle.

  19. 8.4 Special Right Triangles

  20. Theorem 8.6: ________________________ ___________________________________ ___________________________________ 45 45

  21. Theorem 8.7: _______________________ ___________________________________ ___________________________________ 60 30

  22. Examples: 45 12 y y 14 45 y x

  23. Examples: 45 y y 45 y x

  24. Examples: 60 60 y x 5 x 30 30 y

  25. Examples: 60 60 y x x 30 30 y

  26. The diagonal of a square is 6 find the perimeter of the square. 6

  27. The perimeter of an Equilateral triangle is 30, find the length of an altitude.

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