The

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The
Pythagorean
Theorem
c
a
b
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This is a right triangle
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We call it a right triangle because it contains a
right angle.
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The measure of a right angle is 90o
90o
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in the
The little square
angle tells you it is a
right angle.
90o
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About 2,500 years ago, a Greek mathematician
named Pythagorus discovered a special
relationship between the sides of right triangles.
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Pythagorus realized that if you have a right
triangle,
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and you square the lengths of the two sides that
make up the right angle,
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and add them together,
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you get the same number you would get by squaring
the other side.
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Is that correct?
?
?
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It is. And it is true for any right triangle.
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The two sides which come together in a right
angle are called
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The two sides which come together in a right
angle are called
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The two sides which come together in a right
angle are called
legs.
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The lengths of the legs are usually called a and
b.
a
b
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The side across from the right angle
is called the
hypotenuse.
a
b
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And the length of the hypotenuse
is usually labeled c.
c
a
b
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The relationship Pythagorus discovered is now
called The Pythagorean Theorem
c
a
b
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The Pythagorean Theorem says, given the right
triangle with legs a and b and hypotenuse c,
c
a
b
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then
c
a
b
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Find the length of a diagonal of the rectangle
?
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Find the length of a diagonal of the rectangle
?
c
b 8
a 15
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Find the length of a diagonal of the rectangle
17
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Practice using The
Pythagorean Theorem to solve these right
triangles
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13
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(No Transcript)
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(a)
(c)
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9
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Pythagorean Triples

• There are cases when the lengths of the sides of
  a right-angled triangle have integral values
• Whole numbers only (No Fractions)

• The 3, 4, 5 right-angled triangle is such a case

The numbers 3, 4 and 5 are said to form a
Pythagorean Triple
52 32 42
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Pythagorean Triples

• There are an infinite number of Pythagorean
  triples

• Here are two more examples

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Summary

• Find the legs and hypotenuse.
• Square the legs (this is a and b)
• Add them together
• Square root them
• This is the length of the hypotenuse
  (this is c)