1. Warm up: Think About it!
If the red, blue and green squares were made of solid gold; would you rather have the red square or both the blue and green square? Why or why not? We will discuss this at the end of class.

2. The
Pythagorean
Theorem c a b

3. This is a right triangle:

4. We call it a right triangle because it contains a right angle.

5. The measure of a right angle is 90o

6. The little square
in the
angle tells you it is a
right angle.
90o

7. About 2,500 years ago, a Greek mathematician named Pythagoras discovered a special relationship between the sides of right triangles.

8. The two sides which come together in a right angle are called
legs.
leg
leg

9. The lengths of the legs are usually called a and b.

10. The side across from the right angle is called the
hypotenuse. c a
Remember the hypotenuse is opposite the right angle. The hypotenuse is usually labeled with a c. b

11. leg c
hypotenuse. a b
leg

12. Remember we can determine the length of sides based on squares
Look at the squares that make up the sides of the yellow triangle. Based on the squares and what we know about square roots, what is the length of side a? Side b? Side c?
Do you see any relationships?

13. The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c,

14. Pythagorus realized that if you have a right triangle,3 4 5

15. and you square the lengths of the two sides that make up the right angle,3 4 5

16. and add them together, 3 4 5

17. you get the same number you would get by squaring the other side.3 4 5

18. It is. And it is true for any right triangle. Test it!8 6 10

19. It is. And it is true for any right triangle.8 6 10

20. The relationship Pythagorus discovered is now called The Pythagorean Theorem:b

21. then c a b

22. Warm up: Think About it!
If the red, blue and green squares were made of solid gold; would you rather have the red square or both the blue and green square? Why or why not? What did you decide?