2. Course 3 4-8 The Pythagorean Theorem OBJECTIVE January 23, 2014 In our study of THE PYTHAGOREAN THEORM (Readiness) the students will be able to Calculate Square Roots (COMPREHENSION) and show what they learned by Applying the Pythagorean Theorem. (COMPREHENSION)

3. Suzy wants to fence in her yard that is 576 square feet. How many feet of fencing will she need to surround her yard? 576 ft² 1)

5. Suzy wants to fence in her yard that is 576 square feet. How many feet of fencing will she need to surround her yard? 576 ft² 1) x x x = x = 24 fencing = 24 x 4 96 feet of fencing

6. Wednesday A large pot has a diameter of 7 inches and is 17 inches tall. If it is half filled with water, about how many cubic inches of water are in the pot? Round your answer to the nearest hundredth. Which irrational number is closest to 12? 7 17 8.5 326.95

7. Modeling the Pythagorean Theorem 1.Use the Cuisenaire Rods® to build a square on each side of the triangle on your paper. 2.Find three different ways of showing that the combined area of the two smaller squares is the same as the largest square.

8. 1.Use the Cuisenaire Rods® to build a square on each side of the triangle on your paper.

9. 2. With your group, find three different ways of showing that the combined area of the two smaller squares is the same as the largest square. (Rearrange the pink and green rectangles so that they fit ON TOP OF the yellow square.)

10. 4 16 u 2 3 9 u 2

11. 4 16 u 2 3 9 u 2 5 25 u 2

12. Course 3 4-8 The Pythagorean Theorem http://nbclearn.com/nfl/cuecard/51220

13. Course 3 4-8 The Pythagorean Theorem Proof

14. Course 3 4-8 The Pythagorean Theorem Pythagoras was born on the Aegean island of Samos. He is best known for the Pythagorean Theorem, which relates the side lengths of a right triangle.

15. What is a right triangle? It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse. leg hypotenuse right angle

16. The Pythagorean Theorem In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then a 2 + b 2 = c 2. Note: The hypotenuse, c, is always the longest side.

17. 1. The measures of three sides of a triangle are given below. Determine whether each triangle is a right triangle. 7, 3, and 8 Which side is the biggest? 8 This must be the hypotenuse (c). Plug your information into the Pythagorean Theorem. It doesn’t matter which number is a or b.

18. 9 + 49 = 64 ? 58 = 64 ? This is NOT true, it is NOT a right triangle. Sides: 7, 3, and 8 3 2 + 7 2 = 8 2

19. Determine whether the triangle is a right triangle given the sides 9, 15, and 12 1.Yes 2.No 3.Purple 9 2 + 12 2 = 15 2 81 + 144 = 225

20. Baseball Problem A baseball “diamond” is really a square. You can use the Pythagorean theorem to find distances around a baseball diamond.

21. Baseball Problem The distance between consecutive bases is 90 feet. How far does a catcher have to throw the ball from home plate to second base?

22. Baseball Problem To use the Pythagorean theorem to solve for x, find the right angle. Which side is the hypotenuse? Which sides are the legs? a 2 + b 2 = c 2 Now use: a 2 + b 2 = c 2

23. Baseball Problem Solution The hypotenuse is the distance from home to second, or side x in the picture. The legs are from home to first and from first to second. Solution: x 2 = 90 2 + 90 2 = 16,200 x = 127.28 ft

24. Course 3 4-8 The Pythagorean Theorem Check It Out: Example 1A 5 12 c 13 = c Pythagorean Theorem Substitute for a and b. a 2 + b 2 = c 2 5 2 + 12 2 = c 2 25 + 144 = c 2 169 = c Simplify powers. Solve for c; c = c 2. Find the length of the hypotenuse to the nearest hundredth.