Introduction to the Pythagorean Theorem

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Introduction to the Pythagorean Theorem
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HOW IS THE PYTHAGOREAN THEOREM USED IN EVERYDAY
LIFE?

• The access ramp will be covered with an
  all-weather carpet. Would you be able to find
  the area of the carpet needed?

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What Is The Pythagorean Theorem?

• The Pythagorean Theorem is
• A2 B2 C2
• It is used when you are finding the missing sides
  of a right triangle.

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Who Came Up With This Theorem?

• Pythagoras was a teacher and a philosopher
• Pythagoras lived during the 6th century B.C. on
  the island of Samos

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What Does The Theorem Mean?

• Pythagoras found out that for a right triangle
  the square of the hypotenuse is equal to the sum
  of the squares of the other two sides
• a and b are the legs, while c is the hypotenuse.
  The hypotenuse is located opposite the right
  angle and will be the longest side.

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In Other Words

• The green square's area (with area C2) equals the
  sum of two others. It is exactly the yellow
  square's area (A2) plus the blue square's (B2).

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Pythagorean Theorem In Action!

• Watch as this animation demonstrates what the
  theorem means.
• The area of the squares on the legs are brought
  together to form one square on the hypotenuse.

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Watch The Following Video Clip

• This will give you a few examples of the
  Pythagorean theorem in everyday life.

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Use the Pythagorean Theorem to solve this problem.

• The shaded surface of this access ramp will be
  covered with all weather carpet. Find the area
  of the carpet needed.
• Draw out the triangular prism on your paper and
  solve.

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Solution

• Was your answer one of the following?
• A) 12
• B) 32
• C) 40
• D) 48
• E) 96

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How to Solve

• First we needed to find the length of the
  hypotenuse.

A2 B2 C2 42 32 C2 16 9 C2 25 C2
Find the square root of each side. C 5
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Find the Area of the shaded surface.

• To find the area of a rectangle take base times
  height.
• Our final answer will be
• 40 units squared.
• Therefore you would need 40 square feet of carpet
  to cover the ramp.

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Summary

• Pythagorean Theorem is A2 B2 C2
• Now you should have a good idea what the
  Pythagorean Theorem is and how it works.
• As you can see it is used in everyday life.
• We will be doing more work with it later on.