Using the Pythagorean Theorem

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Using the Pythagorean Theorem

• Tammy L Jones
• tammyjones_at_tljconsultinggroup.com

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Whats the Connection?

• Number rules the universe.
• Number is the ruler of forms and ideas, and the
  cause of gods and demons.
• Every man has been made by God in order to
  acquire knowledge and contemplate.
• Geometry is knowledge of the eternally existent.
• Number is the within of all things.
• There is geometry in the humming of the strings.
• Time is the soul of this world.

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Pythagoras

• Questions for investigation
• Who was he?
• What did he do?
• What secret did he have?

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Vocabulary
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Vocabulary
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Your Turn

• Right triangle
• Hypotenuse
• Leg

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An Investigation

• Cooperative Groups
• Part will use Cuisenaire rods
• Part will use linking cubes
• Then to graph paper

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The manipulatives.
Unit of measure one cube
Unit of measure centimeters
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Engineering Graph paper
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The Investigation

• Create a right triangle whose sides are 3, 4,
  and 5.
• Trace it.
• Create a square on each side of the triangle.
• Complete the chart.
• Discuss any patterns you see.

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Continuing

• Now repeat the activity for a triangle with side
  lengths 6, 8, and 10.
• Lets have a grand discussion!
• Think about a 5, 12, and 13 right triangle.
• What do you think about the areas of the squares
  on these sides?
• Verify your guess on the graph paper.

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The Pythagorean Theorem
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Can you state the Pythagorean Theorem in words?
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Practice

• If a right triangles legs are 7 units and 24
  units, what is the length of the
  hypotenuse?11 60 61

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More practice.

• If the hypotenuse of a right triangle has the
  length 41 cm and one leg is 40 cm, what is the
  length of the other leg?

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Looking at it another way

• Is a triangle whose sides have the lengths 11,
  60, and 61 a right triangle? How can you verify
  this?

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An application
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TCAP Practice

• Pythagorean Theorem 8th Grade