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THE PYTHAGOREAN THEOREM

THE PYTHAGOREAN THEOREM. . . HOW WILL YOU SOLVE YOUR PROBLEMS IN LIFE?. GET YOUR GRAPHIC ORGANIZERS . Pythagorean Theorem. What is it and how does it work? a 2 + b 2 = c 2. Who is this Man? . Pythagorean Theorem. Find the legs and hypotenuse Square the legs (this is a and b)

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THE PYTHAGOREAN THEOREM

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  1. THE PYTHAGOREANTHEOREM .

  2. HOW WILL YOU SOLVE YOUR PROBLEMS IN LIFE?

  3. GET YOUR GRAPHIC ORGANIZERS

  4. Pythagorean Theorem • What is it and how does it work? • a2 + b2 = c2

  5. Who is this Man?

  6. Pythagorean Theorem • Find the legs and hypotenuse • Square the legs (this is a and b) • Add them together • Square root them • This is the length of the hypotenuse (this is c)

  7. The Right Triangle hypotenuse leg leg Right angle

  8. 1. Square both legs 1 2 3 4 5 6 7 8 4 ft 11 9 10 12 13 14 16 15 3 ft 4ft 1 2 3 4 5 6 3 ft 7 8 9

  9. 2. Count the total squares 1 2 3 4 5 6 7 8 4 ft 11 9 10 12 13 14 16 15 3 ft 4ft 1 2 3 9 + 16 = 25 4 5 6 3 ft 7 8 9

  10. 21 16 22 1 2 3 4 23 17 11 18 24 12 6 5 6 7 8 13 19 7 25 1 4 ft 11 8 14 20 9 10 12 2 3 15 9 13 14 16 15 4 3 ft 10 4ft 5 1 2 3 9 + 16 = 25 4 5 6 3 ft 7 8 9 3. Put that number of squares on the hypotenuse

  11. 21 16 22 1 2 3 4 23 17 11 18 24 12 6 5 6 7 8 13 19 7 25 1 4 ft 11 8 14 20 9 10 12 2 3 15 9 13 14 16 15 4 3 ft 10 4ft 5 1 2 3 9 + 16 = 25 4 5 6 3 ft 7 8 9 4. Count the number of squares that touch the hypotenuse. # = 5

  12. 21 16 22 1 2 3 4 23 17 11 18 24 12 6 5 6 7 8 13 19 7 25 1 4 ft 11 8 14 20 9 10 12 2 3 15 9 13 14 16 15 4 3 ft 10 4ft 5 1 2 3 9 + 16 = 25 4 5 6 3 ft 7 8 9 5.That number is the length of the hypotenuse. # = 5 Length = 5

  13. Summary • Find the legs and hypotenuse. • Square the legs (this is a and b) • Add them together • Square root them • This is the length of the hypotenuse (this is c)

  14. The Pythagorean Theorem and BaseballYou've just picked up a ground ball at first base, and you see the other team's player running towards third base. How far do you have to throw the ball to get it from first base to third base, and throw the runner out?

  15. Real World Applications

  16. Square and Square Roots Start Square it Root it Result

  17. Simplify each root below and identify as a positive root or a negative root.

  18. To find the hypotenuse, solve for c. 1) 2) a = 3, b = 4, find c. Find the Hypotenuse

  19. Example: Find a leg • You will not always solve for the hypotenuse (c). Sometimes you will have to find a leg (a or b). • Example:

  20. Practice: Pythagorean Theorem

  21. FACTS ON THE PYTHAGOREAN THEOREM Euclid proved the Pythagorean Theorem Descartes writes La Geometrie Plato was influenced by Pythagoras. Plato Influenced Aristotle. The Babylonians and Egyptians were the ancient cultures to discover the right triangle problem solving technique.

  22. Are you ready to rumble!!!

  23. Resources • http://www.gpb.org/education • Music by Coldplay “Clocks”

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