9.2 The Pythagorean Theorem

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9.2 The Pythagorean Theorem

• Did Pythagoras of Samos discover the Pythagorean
  theorem?

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The Pythagorean Theorem

• In a Right triangle, the sum of the squares of
  the legs is equal to the square of the
  hypotenuse.

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The Pythagorean Theorem

• In a Right triangle, the sum of the squares of
  the legs is equal to the square of the
  hypotenuse.

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Pythagorean Triples

• If the sides of a Right triangle are integers,
  then the sides are known as a Pythagorean Triple
• 7, 24, 25
• Do you know any other ?

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Pythagorean Triples

• If the sides of a Right triangle are integers,
  then the sides are known as a Pythagorean Triple
• 7, 24, 25
• Do you know any other ?
• 3, 4, 5
• 5, 12, 13

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Solve for x

• A Right Triangle

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Solve for x

• A Right Triangle

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Area and the Right Triangle

• Area equals ½ altitude times base A½ab
• b and a are the same as the legs of a Right
  triangle.

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2 poles are supported by 100ft cables 50 ft from
the ground

• How far are the poles apart?

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2 poles are supported by 100ft cables 50 ft from
the ground

• How far are the poles apart?

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2 poles are supported by 100ft cables 50 ft from
the ground

• How far are the poles apart?

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Solve for y

• Use the Right Triangle

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Solve for y

• Use the Right Triangle

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Homework

• Page 538 541
• 8 24 even,
• 25 - 31, 33, 34,
• 39, 40

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• The Pythagorean theorem is named after the Greek
  mathematician Pythagoras, who by tradition is
  credited with its discovery and proof, although
  it is often argued that knowledge of the theorem
  predates him. There is evidence that Babylonian
  mathematicians understood the formula, although
  there is little surviving evidence that they
  fitted it into a mathematical framework.
  http//en.wikipedia.org/wiki/Pythagorean_theorem
  Proof_using_similar_triangles