Pythagorean Theorem What is it and how does

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Pythagorean Theorem • What is it and how does it work? • a 2

Pythagorean Theorem • What is it and how does it work? • a 2 + b 2 = c 2

Pythagorean Theorem • • • Find the legs and hypotenuse Square the legs (this

Pythagorean Theorem • • • 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)

The Right Triangle hypotenuse leg Right angle leg

The Right Triangle hypotenuse leg Right angle leg

1. Square both legs 1 2 3 4 5 6 7 8 9 10

1. Square both legs 1 2 3 4 5 6 7 8 9 10 11 12 4 ft 13 14 15 4 ft 16 3 ft 1 2 3 4 5 6 7 8 9 3 ft

2. Count the total squares 1 2 3 4 5 6 7 8 9

2. Count the total squares 1 2 3 4 5 6 7 8 9 10 11 12 4 ft 13 14 15 4 ft 16 9 + 16 = 25 3 ft 1 2 3 4 5 6 7 8 9 3 ft

3. Put that number of squares on the hypotenuse 21 16 22 11 17

3. Put that number of squares on the hypotenuse 21 16 22 11 17 23 6 12 18 24 7 13 19 25 1 1 2 3 4 8 14 20 2 3 15 5 6 7 8 9 4 10 9 10 11 12 4 5 ft 13 14 15 16 3 4 ft 1 ft 2 3 9 + 16 = 25 4 5 6 7 8 9 3 ft

4. Count the number of squares that touch the hypotenuse. 21 16 1 5

4. Count the number of squares that touch the hypotenuse. 21 16 1 5 9 13 22 11 17 23 6 12 18 24 7 13 19 25 1 2 3 4 8 14 20 2 3 15 6 7 8 9 4 10 10 11 12 4 5 ft 14 15 16 3 #=5 4 ft 1 ft 2 3 9 + 16 = 25 4 5 6 7 8 9 3 ft

5. That number is the length of the hypotenuse. 21 16 1 5 9

5. That number is the length of the hypotenuse. 21 16 1 5 9 13 22 11 17 23 6 12 18 24 7 13 19 25 1 2 3 4 8 14 20 2 3 15 6 7 8 9 4 10 10 11 12 4 5 ft 14 15 16 3 #=5 4 ft Length = 5 1 ft 2 3 9 + 16 = 25 4 5 6 7 8 9 3 ft

Summary • • • Find the legs and hypotenuse. Square the legs (this is

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)

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