1. 8-6 The Pythagorean Theorem Pythagorus (say "pie-thag-or-us") of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. He made important developments in mathematics, astronomy, and the theory of music. Pythagoras spent much of his life studying mathematics and formed a special school where members followed strict rules, such as never eating meat. Pythagoras believed that everything in the world could be explained by numbers and his school worked hard to try to learn enough about numbers to be able to understand the universe.

2. How we use the Pythagorean theorem To find the missing side length in a right triangle when you know two side lengths To find the missing side length in a right triangle when you know two side lengths To determine if three given side lengths form a right triangle To determine if three given side lengths form a right triangle

3. Only works with right Triangles leg hypotenuse c 2 = a 2 + b 2 Longest side Right angle

4. c a b c 2 = a 2 + b 2

6. 15 in 8 in x c 2 =a 2 +b 2 x 2 =15 2 +8 2 X 2 =225+64 X 2 =289 X = 17 Find a missing side length

7. 4 cm y c 2 =a 2 +b 2 y 2 =4 2 +4 2 y 2 =16+16 y 2 =32 y = 5.66 Find a missing side length

8. 25 m 20 m c 2 =a 2 +b 2 25 2 =20 2 +x 2 625=400+x 2 625-400 =x 2 225 =x 2 15 = x x Find a missing side length

9. 12 m 15 m y c 2 =a 2 +b 2 15 2 = 12 2 +x 2 225 = 144+x 2 225 - 144 =x 2 81 =x 2 9 = x Find a missing side length

10. Determine if the three given sides form a right Triangle 6, 8, 10 C 2 = a 2 + b 2 10 2 = 6 2 + 8 2 100 = 36 + 64 100 = 100 Yes it is a Right Triangle

11. 4, 8, 7 C 2 = a 2 + b 2 8 2 = 7 2 +4 2 64 = 49 + 16 64 = 65 No it is NOT a right Triangle