1. 7.1 – Apply the Pythagorean Theorem

2. In your group, do the following: 1. Find the area of one of the four right triangles baba abab b a c

3. In your group, do the following: 2. Find the TOTAL area for all four right triangles baba abab b a c 2 2ab

4. In your group, do the following: 3. Find the area of the tilted square baba abab b a c A = s 2 A = c 2

5. In your group, do the following: 4. Find the area of the large square baba abab b a c A = s 2 A = (a+b) 2 A = (a+b)(a + b) A = a 2 + 2ab + b 2

6. In your group, do the following: 5. Write an equation to show the area of the tilted square plus the four triangles equal the area of the large square and simplify baba abab b a c c 2 + 2ab = a 2 + 2ab + b 2 c 2 = a 2 + b 2 Sound familiar?

7. Pythagorean Theorem: leg hypotenuse a b c c 2 = a 2 + b 2 (hypotenuse) 2 = (leg) 2 + (leg) 2 If a triangle is a right triangle, then (hypotenuse) 2 = (leg) 2 + (leg) 2

8. 1. Find the value of x. c 2 = a 2 + b 2 x 2 = 15 2 + 36 2 x 2 = 225 + 1296 x 2 = 1521 x = 39 H

9. 1. Find the value of x. c 2 = a 2 + b 2 x 2 = 4 2 + 9 2 x 2 = 16 + 81 x 2 = 97 H

10. 1. Find the value of x. c 2 = a 2 + b 2 x 2 = 6 2 + 3 2 x 2 = 36 + 9 x 2 = 45 H

11. 1. Find the value of x. c 2 = a 2 + b 2 17 2 = x 2 + 8 2 289 = x 2 + 64 225 = x 2 H

12. 1. Find the value of x. c 2 = a 2 + b 2 27 2 = x 2 + 9 2 729 = x 2 + 81 648 = x 2 H

13. 1. Find the value of x. c 2 = a 2 + b 2 42 2 = x 2 + 36 2 1764 = x 2 + 1296 468 = x 2 H

14. 2. Find the area of the isosceles triangle. c 2 = a 2 + b 2 10 2 = h 2 + 8 2 100 = h 2 + 64 36 = h 2 8 8 8 in 2 H H

15. 2. Find the area of the isosceles triangle. c 2 = a 2 + b 2 12 2 = h 2 + 4 2 144 = h 2 + 16 128 = h 2 4 cm 2 H

16. 2. Find the area of the isosceles triangle. c 2 = a 2 + b 2 44 2 = h 2 + 24 2 1936 = h 2 + 576 1360 = h 2 24 m 2 24 H

17. 7.2 – Converse of the Pythagorean

18. Pythagorean Theorem Converse: If c 2 = a 2 + b 2, then the triangle is a right triangle a b c

19. Acute Triangle: If c 2 < a 2 + b 2, then the triangle is acute a b c

20. Obtuse Triangle: If c 2 > a 2 + b 2, then the triangle is obtuse a b c

21. For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! c 2 = a 2 + b 2 17 2 = 8 2 + 15 2 289 = 64 + 225 289 = 289 8 + 15 > 17 8 + 17 > 15 15 + 17 > 8 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE a. 8, 15, 17

22. 3 + 4 > 9 b. 3, 4, 9 Triangle: YES or NO ACUTE, RIGHT, or OBTUSE 7 > 9 For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK!

23. c 2 = a 2 + b 2 196 = 100 + 121 196 221 c. Triangle: YES or NO ACUTE, RIGHT, or OBTUSE For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! 10, 11, 14 10 + 11 > 14 10 + 14 > 11 11 + 14 > 10 14 2 = 10 2 + 11 2 <

24. c 2 = a 2 + b 2 61 = 25 + 36 61 = 61 d. For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! Triangle: YES or NO ACUTE, RIGHT, or OBTUSE 5 + 6 > 7.8 5 + 7.8 > 6 6 + 7.8 > 5

25. c 2 = a 2 + b 2 144 = 13 + 100 144 113 e. For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! Triangle: YES or NO ACUTE, RIGHT, or OBTUSE 3.6 + 10 > 12 3.6 + 12 > 10 10 + 12 > 3.6 >

26. c 2 = a 2 + b 2 37.21 = 18.49 + 27.04 37.21 45.53 f. 4.3, 5.2, 6.1 For each set of numbers, determine whether the numbers represent the side lengths of a triangle. If so, is the triangle acute, right, or obtuse. SHOW WORK! Triangle: YES or NO ACUTE, RIGHT, or OBTUSE 4.3 + 5.2 > 6.1 4.3 + 6.1 > 5.2 5.2 + 6.1 > 4.3 <

27. 7.1 7.2 436-439 444-445 3, 5, 13-17 odd, 24, 26, 31, 39, 40 3-7 odd, 15-21 odd, 25 HW Problem 7.1 #26 Ans: c 2 = a 2 + b 2 5 2 = a 2 + 3 2 25 = a 2 + 9 16 = a 2 a HH 4 = a c 2 = a 2 + b 2 x 2 = 4 2 + 7 2 x 2 = 16 + 49 x 2 = 65