Example 3: Find the value of the missing leg and hypotenuse on a scratch piece of paper then fill in the blanks below.

• The Pythagorean Theorem is ______?______
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  Check Your Answer

  a² + b² = c²
  
• Substitute x in for the length of the missing leg and x + 1 for the length of the hypotenuse. ____?____
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  Check Your Answer

  a² + x² = (x + 1)²
  
• Substitute the known value for a.____?___
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  Check Your Answer

  9² + x² = (x + 1)²
  
• Simplify.  ________?________
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  Check Your Answer

  81 + x² = x² + 2x + 1
  
• Use the subtraction property to isolate.___?_____
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  Check Your Answer

  81 - 1 + x² - x² = x² + 2x + 1 - 1
  
• Simplify. _____?_____
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  Check Your Answer

  80 = 2x
  
• Solve for x .____?_____
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  Check Your Answer

  40 = x
  
• One leg has a length of ___?___ and the other leg has a length of ___?___.
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  Check Your Answer

  9, 40
  
• The hypotenuse has a length of  ____?____
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  Check Your Answer

  x + 1 = 40 + 1 = 41