The Pythagorean Theorem

1
The Pythagorean Theorem
a2 b2 c2

• A Geometric Approach

2
Every right triangle consists of 2 legs and a
hypotenuse.
hypotenuse
leg
hypotenuse
leg
leg
hypotenuse
leg
leg
leg
3
The hypotenuse is the longest side in a right
triangle and it is opposite the right angle.
hypotenuse
leg
hypotenuse
leg
leg
hypotenuse
leg
leg
leg
4
Consider the following right triangle
5 in
3 in
4 in
5
Lets build squares off each of the 3 sides in
the triangle.
5 in
3 in
4 in
6
5 in
3 in
4 in
7
5 in
3 in
4 in
8
5 in
3 in
4 in
9
Now lets find the area of each square.
5 in
5 in
3 in
4 in
3 in
4 in
10
Now lets find the area of each square.
5 in
5 in
3 in
4 in
3 in
4 in
11
Now lets find the area of each square.
5 in
5 in
9 in2
4 in
4 in
12
Now lets find the area of each square.
5 in
5 in
9 in2
16 in2
13
Now lets find the area of each square.
25 in2
9 in2
16 in2
14
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.
25 in2
9 in2
16 in2
15
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.
25 in2
9 in2
16 in2
16
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.
25 in2
9 in2
16 in2
17
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.
25 in2
9 in2
16 in2
18
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.
25 in2
9 in2
16 in2
19
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.
25 in2
16 in2
9 in2
20
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.

25 in2
16 in2

9 in2
21
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.


22
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.


23
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.


24
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.


25
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.


26
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.


27
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.


28
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.


29
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.


30
The Pythagorean Theorem states that the sum of
the areas of the two smaller squares should equal
the area of the larger square.

31
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
? in
9 in
12 in
32
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
Find the area of each square that can be built
off each leg.
? in
9 in
12 in
33
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
Find the area of each square that can be built
off each leg.
? in
81 in2
9 x 9
9 in
12 in
34
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
Find the area of each square that can be built
off each leg.
? in
81 in2
9 x 9
9 in
12 in
144 in2
12 x 12
35
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
? in2
? in
81 in2
9 x 9
9 in
The sum of the areas of these 2 squares should
equal the area of the third square.
12 in
144 in2
12 x 12
36
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
? in2
? in
81 in2
9 x 9
9 in
The sum of the areas of these 2 squares should
equal the area of the third square.
12 in
144 in2
12 x 12
37
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
? in2
? in
81 in2
9 in
The sum of the areas of these 2 squares should
equal the area of the third square.
12 in
144 in2
38
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
? in2
81 in2
9 in
? in
12 in
The sum of the areas of these 2 squares should
equal the area of the third square.
144 in2
39
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
12 in
? in2


144 in2
81 in2
9 in
? in
The sum of the areas of these 2 squares should
equal the area of the third square.
40
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
12 in
225 in2


144 in2
81 in2
9 in
? in
The sum of the areas of these 2 squares should
equal the area of the third square.
41
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
12 in
225 in2
? in


144 in2
81 in2
9 in
? in
? in
If the area of this square is 225 in2, then how
long is each side?
42
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
12 in
? in
225 in2


144 in2
81 in2
9 in
? in
? in
If the area of this square is 225 in2, then how
long is each side?
43
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
12 in
15 in
225 in2


144 in2
81 in2
9 in
? in
15 in
If the area of this square is 225 in2, then how
long is each side?
44
Use the Pythagorean Thm. to determine the length
of the hypotenuse.
225 in2
? in
81 in2
15 in
9 in
9 in
12 in
81 in2 144 in2 225 in2
12 in
144 in2
45
Practice Time!
46
1)Use the Pythagorean Thm. to determine the
length of the hypotenuse.
? in
12 in
16 in
47
1)Use the Pythagorean Thm. to determine the
length of the hypotenuse.
? in2
? in
? in
144 in2
12 x 12
12 in
9 in
12 in
16 in
256 in2
16 x 16
48
1)Use the Pythagorean Thm. to determine the
length of the hypotenuse.
400 in2
? in
? in
144 in2
12 in
9 in
12 in
16 in
144in2 256in2 400in2
256 in2
49
1)Use the Pythagorean Thm. to determine the
length of the hypotenuse.
400 in2
? in
? in
144 in2
20 in
12 in
12 in
9 in
16 in
12 in
16 in
144in2 256in2 400in2
256 in2
50
2)Use the Pythagorean Thm. to determine the
length of the hypotenuse.
? in
8 in
10 in
51
2)Use the Pythagorean Thm. to determine the
length of the hypotenuse.
? in2
? in
64 in2
8 x 8
8 in
12 in
9 in
12 in
10 in
16 in
100 in2
10 x 10
52
2)Use the Pythagorean Thm. to determine the
length of the hypotenuse.
164 in2
? in
64 in2
8 in
12 in
9 in
12 in
10 in
16 in
64in2 100in2 164in2
100 in2
53
2)Use the Pythagorean Thm. to determine the
length of the hypotenuse.
164 in2
64 in2
12.8 in
8 in
12 in
9 in
8 in
10 in
12 in
10 in
16 in
64in2 100in2 164in2
100 in2
54
3)Use the Pythagorean Thm. to determine the
length of the hypotenuse.
? in
6 in
11 in
55
3)Use the Pythagorean Thm. to determine the
length of the hypotenuse.
? in2
? in
36 in2
6 x 6
6 in
8 in
12 in
9 in
12 in
11 in
10 in
16 in
121 in2
11 x 11
56
3)Use the Pythagorean Thm. to determine the
length of the hypotenuse.
157 in2
? in
36 in2
6 in
8 in
12 in
9 in
12 in
11 in
10 in
16 in
36in2 121in2 157in2
121 in2
57
3)Use the Pythagorean Thm. to determine the
length of the hypotenuse.
157 in2
? in
36 in2
12.5 in
6 in
6 in
8 in
12 in
9 in
11 in
12 in
11 in
10 in
16 in
36in2 121in2 157in2
121 in2
58
4)Use the Pythagorean Thm. to determine the
length of the leg.
Caution This problem is a little different
because you have to find the leg, not the
hypotenuse.
7 in
? in
5 in
59
4)Use the Pythagorean Thm. to determine the
length of the leg.
49 in2
7 x 7
6 in
? in2
5 in
6 in
8 in
12 in
9 in
12 in
? in
11 in
10 in
16 in
25 in2
5 x 5
60
4)Use the Pythagorean Thm. to determine the
length of the leg.
49 in2
6 in
24 in2
5 in
6 in
8 in
12 in
9 in
Note You should be subtracting.
12 in
? in
11 in
10 in
16 in
49in2 - 25in2 24in2
25 in2
61
4)Use the Pythagorean Thm. to determine the
length of the leg.
49 in2
6 in
24 in2
4.8 in
7 in
5 in
6 in
8 in
12 in
9 in
5 in
12 in
? in
11 in
10 in
16 in
49in2 - 25in2 24in2
25 in2
62
The End