today we reviewed the Pythagorean Theorem and there was one sheet handed out to the B and D class and two handed out to the C class. B and D make sure both sides are done, C make sure the front of each is done.

1. a
b
c
222
cba 

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
90o

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

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,
2
42
3
3
4
5

9. and add them together,
3
4
5
2
42
3 22
43 

10. 22
43 
you get the same number
you would get by squaring
the other side.
222
543 
3
4
5

11. Is that correct?
222
543 
?
25169 
?

12. It is. And it is true for any
right triangle.
8
6
10222
1086 
1006436 

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
a
b
is called the

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

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

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

21. then
a
b
c
.222
cba 

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

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

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

25. 482
Using The Pythagorean
Theorem,
48
36
c
362
+ = c2

26. Why?Can you see that we have a
right triangle?
48
36
c
482
362
+ = c2

27. Which side is the hypotenuse?Which sides are the legs?
48
36
c
482
362
+ = c2

28.  22
3648
Then all we need to do is
calculate:
12962304
3600 2
c

29. And you end up 60 miles from
where you started.
48
36
60
So, since c2
is 3600, c is 60.So, since c2
is 3600, c is

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

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

32. 222
cba  222
815 c 2
64225 c 2892
c 17c
b = 8
a = 15
c

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

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

35. 5
12
c = 13

36. 10
b
26

37. 10
b
26
= 24
(a)
(c)
222
cba 
222
2610  b
676100 2
 b
1006762
b
5762
b
24b

38. 12
b
15
= 9