1. The
Pythagorean
Theorem c a b

2. This is a right triangle:

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

4. The measure of a right angle is 90o

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

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

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

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

9. and add them together, 3 4 5

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

11. Is that correct? ? ?

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

13. The two sides which come together in a right angle are called

14. The two sides which come together in a right angle are called

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

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

17. The side across from the right angle is called the
hypotenuse. a b

18. And the length of the hypotenuse is usually labeled c.

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

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

21. then c a b

22. Find the length of a diagonal of the rectangle:
15"
8" ?

23. Find the length of a diagonal of the rectangle:
15"
8" ?
b = 8 c
a = 15

24. b = 8
a = 15 c

25. Find the length of a diagonal of the rectangle:
15"
8" 17

26. Practice using The Pythagorean Theorem to solve these right triangles:

27. 5 12 c
= 13

28. 10 b 26

29. = 24 10 b 26
(a)
(c)

30. 12 b 15
= 9

31. The numbers 3, 4 and 5 are said to form a Pythagorean Triple
Pythagorean Triples
There are cases when the lengths of the sides of a right-angled triangle have integral values
Whole numbers only (No Fractions) 3 4 5
The 3, 4, 5 right-angled triangle is such a case
The numbers 3, 4 and 5 are said to form a Pythagorean Triple
52 =

32. There are an infinite number of Pythagorean triples5 12 13
There are an infinite number of Pythagorean triples
Here are two more examples … 25 7 24

33. Summary Find the legs and hypotenuse.
Square the legs (this is a and b)
Add them together
Square root them
This is the length of the hypotenuse (this is c)