THE PYTHAGOREAN THEOREM

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THE PYTHAGOREAN THEOREM
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What is the Pythagorean Theorem?

• The theorem that the sum of the squares of the
  lengths of the sides of a right triangle is equal
  to the square of the length of the hypotenuse.

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What?

• In simpler terms the Pythagorean Theorem is a
  formula that is used when trying to find a
  missing side in a right triangle.
• The formula is a2 b2 c2
• (hearts and bunnies around this one)

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Review

• In order to use the theorem you must know what a
  right triangle is.
• A right triangle is a triangle that has an angle
  of 90.

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How to use the Pythagorean Theorem

• First make sure the triangle, you are dealing
  with, is a right triangle.
• Make sure you have two side measurements of the
  triangles you are dealing with.

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Quick Hints

• C in the Pythagorean Theorem is always the
  hypotenuse.
• Review The hypotenuse is the side opposite of
  the right angle in a right triangle.
• A and B in the Pythagorean Theorem are the two
  remaining sides. No specific side for either
  variable.

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Practice the Basics
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Use the Theorem

• A6
• B8
• C?
• First, plug the numbers into the formula.
• 62 82 c2 ? Substitute
• 36 64 c2
• 100 c2 ? inverse operation of
  squaring is square root
• 10 c ??100 is 10

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Inverse of c2

• Use a opposite operation to eliminate the square
  in c2 by taking the square root of the sum of A
  and B.
• Square root of 10010
• Plug the solution into the formula.
• 10c

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Final Step

• The final step is to check your work. Check your
  work by plugging the answer back into the
  original formula to make sure the answer is
  correct.
• 6282102 ? Substitute for c
• 3664100 ?
• 100100

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Practice

• Find the length of the hypotenuse.
• a 3 b 4
• a2 b2 c2
• 32 42 c2 substitute a and b
• 9 16 c2 Square a b
• 25 c2 Add a b
• ?25 c Undo the square root
• 5 c Solved!

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Check

• 32 42 c2 ? start with the original equation
• 32 42 52 ? Substitute your answer for C
• 9 16 25 ? simplify
• 25 25 ? it balances!

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Try this one

• 52 122 c2

25 144 c2 169 c2
?169 c2 13 c
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Sometimes they do not come out even

• 62 102 c2

62 102 c2 36 100 c2 136 c2
?136 c 11.661 ? c
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Thats all for today!

• Tomorrow
• Solving for A or B!
• I know you can hardly wait!