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The Pythagorean Theorem

a2 b2 c2

- A Geometric Approach

Every right triangle consists of 2 legs and a

hypotenuse.

hypotenuse

leg

hypotenuse

leg

leg

hypotenuse

leg

leg

leg

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

Consider the following right triangle

5 in

3 in

4 in

Lets build squares off each of the 3 sides in

the triangle.

5 in

3 in

4 in

5 in

3 in

4 in

5 in

3 in

4 in

5 in

3 in

4 in

Now lets find the area of each square.

5 in

5 in

3 in

4 in

3 in

4 in

Now lets find the area of each square.

5 in

5 in

3 in

4 in

3 in

4 in

Now lets find the area of each square.

5 in

5 in

9 in2

4 in

4 in

Now lets find the area of each square.

5 in

5 in

9 in2

16 in2

Now lets find the area of each square.

25 in2

9 in2

16 in2

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

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

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

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

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

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

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

The Pythagorean Theorem states that the sum of

the areas of the two smaller squares should equal

the area of the larger square.

The Pythagorean Theorem states that the sum of

the areas of the two smaller squares should equal

the area of the larger square.

The Pythagorean Theorem states that the sum of

the areas of the two smaller squares should equal

the area of the larger square.

The Pythagorean Theorem states that the sum of

the areas of the two smaller squares should equal

the area of the larger square.

The Pythagorean Theorem states that the sum of

the areas of the two smaller squares should equal

the area of the larger square.

The Pythagorean Theorem states that the sum of

the areas of the two smaller squares should equal

the area of the larger square.

The Pythagorean Theorem states that the sum of

the areas of the two smaller squares should equal

the area of the larger square.

The Pythagorean Theorem states that the sum of

the areas of the two smaller squares should equal

the area of the larger square.

The Pythagorean Theorem states that the sum of

the areas of the two smaller squares should equal

the area of the larger square.

The Pythagorean Theorem states that the sum of

the areas of the two smaller squares should equal

the area of the larger square.

Use the Pythagorean Thm. to determine the length

of the hypotenuse.

? in

9 in

12 in

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

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

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

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

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

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

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

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.

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.

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?

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?

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?

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

Practice Time!

1)Use the Pythagorean Thm. to determine the

length of the hypotenuse.

? in

12 in

16 in

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

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

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

2)Use the Pythagorean Thm. to determine the

length of the hypotenuse.

? in

8 in

10 in

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

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

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

3)Use the Pythagorean Thm. to determine the

length of the hypotenuse.

? in

6 in

11 in

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

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

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

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

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

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

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

The End

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