The document explains the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. It provides examples of using the theorem to calculate the length of the hypotenuse or legs of a right triangle when the other two sides are known. These include using the theorem to calculate the distance between two points if the distances travelled in each direction are known.

1. 2 2 2
a +b =c
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
o
angle is 90
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,
5
3
4

8. and you square the lengths
of the two sides that make
up the right angle,
5
3
2 2
4 3 4

9. and add them together,
5
3
2 2
4 3 +4

10. you get the same number
you would get by squaring
the other side.
5
3
2 2 2
4 3 +4 =5

11. Is that correct?
2 2 ? 2
3 +4 =5
?
9 + 16 = 25

12. It is. And it is true for any
right triangle.
2 2 2
6 + 8 = 10 10
8
36 + 64 = 100
6

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

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

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

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

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

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

21. 2 2 2
then a + b = c .
c
a
b

22. You can use The Pythagorean
Suppose you drive directly
Theorem48 miles,many kinds
west for to solve
of problems.
48

23. Then turn south and drive for
36 miles.
48
36

24. How far are you from where
you started?
48
36
?

25. Using The Pythagorean
Theorem,
2 2 2
48
48 + 36 = c
36
c

26. Can you
Why? see that we have a
right triangle?
2 2 2
48
48 + 36 = c
36
c

27. Which side is the hypotenuse?
sides are the legs?
2 2 2
48
48 + 36 = c
36
c

28. Then all we need to do is
calculate:
2 2
48 + 36 = 2304 +1296 =
2
3600 = c

29. 2
So, you c is 3600, c is from
Andsince end up 60 miles60.
where you started.
48
36
60

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

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

32. 2 2 2
15c = 17 = c
225 = 8
a +b
c 64 289
b=8 c
a = 15

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

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

35. c = 13
5
12

36. b
10
26

37. b = 24
2 2 2 10 (a)
a +b =c
26
2 2 2
10 + b = 26 (c)
2
100 + b = 676
2
b = 676 − 100
2
b = 24
b = 576

38. 12
b= 9
15