The Pythagorean Theorem can also be shown geometrically.

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How does the area of the largest square, alongside the hypotenuse, compare to the areas of the two smaller squares, alongside the legs?

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Hint

What operation are you performing when you move the pieces of the smaller squares into the interior of the largest square?Close Pop Up Interactive popup. Assistance may be required.

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The area of the largest square is equal to the sum of the areas of the two smaller squares.Close Pop Up

Write an algebraic expression that relates the side lengths a, b, and c.

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Hint

How do you find the area of a square if you know the side length?Close Pop Up Interactive popup. Assistance may be required.

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a2 + b2 = c2Close Pop Up

Practice

  1. If a = 3 and b = 4, what is the area of Square A and Square B?

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    Square A = 9 square units
    Square B = 16 square units Close Pop Up
  2. What will be the area of Square C?

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    Square C = 25 square units Close Pop Up
  3. What will be the side length of Square C?

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    c = 5 units Close Pop Up
  4. What will be the perimeter of each square?

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    Perimeter of Square A = 12 units
    Perimeter of Square B = 16 units
    Perimeter of Square C = 20 units Close Pop Up
  5. If a = 5 and b = 12, what are the areas of all three squares?

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    Square A = 25 square units
    Square B = 144 square units
    Square C = 169 square units Close Pop Up
  6. What will be the side length of Square C?

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    c = 13 units Close Pop Up

    7. Consider the figure shown.

  7. What is the area of the smallest square?

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    c = 36 square units Close Pop Up