1. Pythagorean Theorem OBJ: to use the Pythagorean theorem to solve problems

2. Pythagoras Lived in the 500’s B.C was one of the first Greek Mathematical thinkers. Had a group of followers called the Pythagoreans. This group was interested in philosophy but especially interested in music and mathematics, 2 ways of making order out of chaos. Music is noise that makes sense and math is the rules for how the world works.

3. Parts of a Right Triangle leg Legs- connected by right angle leg Hypotenuse- opposite the right angle and always the longest side Hypotenuse

4. Pythagorean Theorem Here’s how it works… a and b are the legs of the right triangle and c is the hypotenuse. So leg 2 +leg 2 =hypotenuse 2

5. Example Find the length of the hypotenuse 15 in 20 in a 2 + b 2 = c 2 leg 2 + leg 2 = hyp 2 15 2 + 20 2 = c 2 225 + 400 = c 2 625 = c 2 25 = c 25 in

6. Example: Find the missing length x in 8 in 10 in a 2 + b 2 = c 2 8 2 + b 2 = 10 2 64 + b 2 = 100 b 2 = 36 b = 6 The side is 6 in

7. Conditional Statement What is a conditional statement? –IF is known as the hypothesis and THEN is the conclusion. For example: If it is windy, then I will wear a coat. Hypothesis: it is windy. Conclusion: I will wear a coat.

8. Pythagorean Theorem If a triangle is a right triangle then a 2 + b 2 = c 2 Converse: When you switch the hypothesis with the conclusion in a conditional statement. Converse of the Pythagorean Theorem If a 2 + b 2 = c 2 then the triangle is a right triangle.

9. Example: Use the converse to determine if if the triangle is a right triangle. 13 in 10 in 8 in a 2 + b 2 = c 2 10 2 + 8 2 = 13 2 100 + 64 = 169 164 = 169 Not a right triangle!