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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You can use The Pythagorean Theorem to solve many
kinds of problems.
Suppose you drive directly west for 48 miles,
48
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Then turn south and drive for 36 miles.
48
36
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How far are you from where you started?
48
36
?
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Using The Pythagorean Theorem,
48
482
362


c2
36
c
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Why?
Can you see that we have a right triangle?
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Which side is the hypotenuse?
Which sides are the legs?
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Then all we need to do is calculate
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And you end up 60 miles from where you started.
So, since c2 is 3600, c is
48
36
60
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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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(No Transcript)
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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)
37
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(a)
(c)
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