5.4

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5.4 Pythagorean Theorem
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GEO-METRY

• geometry is Greek for earth measure
• In ancient Egypt, the Nile flooded every year
• Good for crops / Bad for property boundaries

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GEO-METRY

• The Egyptians had to devise a method for
  re-determining boundaries after each flood
• Greek mathematicians later redeveloped these
  methods and called it ?
• GEOMETRY!!!!!!!!!!!!!!!!!!!!!!

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Pythagoras (569 BC 475 BC)
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Pythagorean Theorem

• For any right triangle, the sum of the squares of
  the lengths of the legs is equal to the square of
  the length of the hypotenuse
• a2b2c2

c
a
b
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Thanks, Mr. Pythagoras!
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Proof (just one of the many)
(A B) ² 4(½AB) C²
A² 2AB B² 2AB C²
A² B² C²
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Hypo what?

• What is a hypotenuse?
• A side of a right triangle
• Where is the hypotenuse?
• Always across from the 90 angle
• It is always the biggest side

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Can a right triangle walk?

• Yes because it has
• LEGS!!!!!
• They are the other two sides of a right triangle
• They are always smaller than the ?
• hypotenuse

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But is it even a triangle?

• Triangle inequality theorem
• The sum of the lengths of any two sides of a
  triangle is greater than the length of the third
  side

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Is it a triangle?

• Do the following lengths make a triangle?
• 3, 3, 8
• 2, 5, 8
• 4, 5, 8
• 3, 4, 4

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What kind of triangle is it?

• C is the biggest side of the triangle
• If c2 gt a2b2 then ?ABC is obtuse
• If c2 lt a2b2 then ?ABC is acute
• If c2 a2b2 then ?ABC is right

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What kind of triangle is it?

• Do the following three segments form a triangle?
  If so, what kind?
• 4, 5, 8
• 3, 4, 5
• 2, 2, 8
• 4, 4, 5

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What is a Pythagorean Triple?

• A hit in baseball that gets a Greek player to
  third base?
• 3 Greek siblings born on the same day?
• 3 whole numbers that are sides of a right
  triangle?

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Examples of Pythagorean Triples

• 3, 4, 5
• Because 5² 3² 4²
• 5, 12, 13
• Because 13² 5² 12²