1. THE PYTHAGOREAN THEOREM

2. What is the Pythagorean Theorem? The theorem that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse.

3. What? In simpler terms the Pythagorean Theorem is a formula that is used when trying to find a missing side in a right triangle. The formula is a 2 + b 2 = c 2 (hearts and bunnies around this one)

4. Review In order to use the theorem you must know what a right triangle is. A right triangle is a triangle that has an angle of 90°.

5. How to use the Pythagorean Theorem First make sure the triangle, you are dealing with, is a right triangle. Make sure you have two side measurements of the triangles you are dealing with.

6. Quick Hints C in the Pythagorean Theorem is always the hypotenuse. Review; The hypotenuse is the side opposite of the right angle in a right triangle. A and B in the Pythagorean Theorem are the two remaining sides. No specific side for either variable.

7. Practice the Basics

8. Use the Theorem A=6 B=8 C=? First, plug the numbers into the formula. 6 2 + 8 2 = c 2  Substitute 36 + 64 = c 2 100 = c 2  inverse operation of squaring is square root 10 = c  100 is 10

9. Inverse of c 2 Use a opposite operation to eliminate the square in c 2 by taking the square root of the sum of A and B. Square root of 100=10 Plug the solution into the formula. 10=c

10. Final Step The final step is to check your work. Check your work by plugging the answer back into the original formula to make sure the answer is correct. 6 2 +8 2 =10 2  Substitute for c 36+64=100  100=100

11. Practice Find the length of the hypotenuse. a = 3 b = 4 a2 a2 + b 2 = c2c2 32 32 + 42 42 = c2c2 substitute a and b 9 + 16 = c2c2 Square a & b 25 = c 2 Add a & b  25 = c “Undo” the square root 5 = cSolved!

12. Check 3 2 + 4 2 = c 2  start with the original equation 3 2 + 4 2 = 5 2  Substitute your answer for C 9 + 16 = 25  simplify 25 = 25  it balances!

13. Try this one 5 2 + 12 2 + = c 2 5 12 ? 25 + 144 + = c 2 169 = c 2  169 = c 2 13 = c

14. Sometimes they do not come out even 6 2 + 10 2 = c 2 10 6 ? 6 2 + 10 2 = c 2 36 + 100 = c 2 136 = c 2  136 = c 11.661  c

15. That’s all for today! Tomorrow Solving for A or B! I know – you can hardly wait!