2. .

3. HOW WILL YOU SOLVE YOUR PROBLEMS IN LIFE?

4. GET YOUR GRAPHIC ORGANIZERS

5. Pythagorean Theorem What is it and how does it work? a 2 + b 2 = c 2

6. Who is this Man?

7. 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)

8. leg hypotenuse Right angle The Right Triangle

9. 1. Square both legs 3 ft 4 ft 3 ft 13 456 78 9 1 2 23 4 5678 910 11 12 1314 15 16

10. 2. Count the total squares 3 ft 4 ft 3 ft 13 456 78 9 1 2 23 4 5678 910 11 12 1314 15 16 9 + 16 = 25

11. 3 ft 4 ft 3 ft 13 456 78 9 1 2 23 4 5678 910 11 12 1314 15 16 9 + 16 = 25 3. Put that number of squares on the hypotenuse 2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25

12. 3 ft 4 ft 3 ft 13 456 78 9 1 2 23 4 5678 910 11 12 1314 15 16 9 + 16 = 25 4. Count the number of squares that touch the hypotenuse. 2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25 # = 5

13. 3 ft 4 ft 3 ft 13 456 78 9 1 2 23 4 5678 910 11 12 1314 15 16 9 + 16 = 25 5.That number is the length of the hypotenuse. 2 4 6 8 10 12 14 16 18 20 22 24 1 3 5 7 9 11 13 15 17 19 21 23 25 # = 5 Length = 5

14. 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)

15. The Pythagorean Theorem and Baseball You'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?

16. Real World Applications

17. StartSquare itRoot itResult Square and Square Roots

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

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

20. 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:

21. Practice: Pythagorean Theorem

22. 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.

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