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Using the Pythagorean Theorem

Tammy L Jones

tammyjones@tljconsultinggroup.com

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What’s 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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PythagorasQuestions 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: centimeters

Unit of measure: one cube

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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.

• Let’s 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 triangle’s 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