2.  Theorem - A general proposition not self-evident but proved by a chain of reasoning.  In math… a theorem is an idea that can be proven true by logical explanation.

5. Let’s look at a right triangle… 5 cm 4 cm 3 cm

6. Each side has a certain length. What if we draw a square out from each side of the triangle? 5 cm 4 cm 3 cm

7. 4 cm 3 cm 5 cm

8. 4 cm 3 cm 5 cm 9 16 25

9. Now…think about the area of a square. How do we find it?

10. 4 cm 3 cm 5 cm 3 3 3 x 3 = 3 2 = 9

11.  After all that, the Pythagorean Theorem comes down to this simple equation.  The length of each side squared must equal the length of the longest side (hypotenuse) squared.  3 2 + 4 2 = 5 2  9 + 16 = 25

12. 6 m 8 m ? A 2 + B 2 = C 2 6 2 + 8 2 = ? 2 36 + 64 = ? 2 100 = ? 2 But remember, the missing side does not equal 100. It’s a number that equals 100 when it’s squared. ? = 10

13. 5 ft 12 ft C A 2 + B 2 = C 2  5 2 + 12 2 = C 2  25 + 144 = 169 C 2 = 169, so C = √169 C = 13

14. 15 in 9 in B When we are missing a leg rather than the hypotenuse, we must be sure to find either A or B in the equation. A 2 + B 2 = C 2  9 2 + B 2 = 15 2  81 + B 2 = 225 225 – 81 = 144  B 2 = 144  B = √144 = 12