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Pythagorean Theorem Explained: How It Works and Its Applications

Learn about the Pythagorean Theorem, a² + b² = c², for finding the legs and hypotenuse of a right triangle. Step-by-step guide to calculating the hypotenuse length. Discover the relationship between the hypotenuse, legs, and right angle.

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Pythagorean Theorem Explained: How It Works and Its Applications

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  1. Pythagorean Theorem • What is it and how does it work? • a2 + b2 = c2

  2. 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)

  3. The Right Triangle hypotenuse leg leg Right angle

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

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

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

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

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

  9. 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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