Warm up: Think About it!

1
Warm upThink About it!

• If the red, blue and green squares were made of
  solid gold would you rather have the red square
  or both the blue and green square? Why or why
  not? We will discuss this at the end of class.

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The
Pythagorean
Theorem
c
a
b
3
This is a right triangle
4
We call it a right triangle because it contains a
right angle.
5
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 Pythagoras discovered a special
relationship between the sides of right triangles.
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The two sides which come together in a right
angle are called
legs.
leg
leg
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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.
c
a
Remember the hypotenuse is opposite the right
angle. The hypotenuse is usually labeled with a c.
b
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c
leg
hypotenuse.
a
b
leg
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Remember we can determine the length of sides
based on squares
Look at the squares that make up the sides of the
yellow triangle. Based on the squares and what
we know about square roots, what is the length of
side a? Side b? Side c? Do you see any
relationships?
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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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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,
17
you get the same number you would get by squaring
the other side.
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It is. And it is true for any right triangle.
Test it!
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It is. And it is true for any right triangle.
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The relationship Pythagorus discovered is now
called The Pythagorean Theorem
c
a
b
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then
c
a
b
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Warm upThink About it!

• If the red, blue and green squares were made of
  solid gold would you rather have the red square
  or both the blue and green square? Why or why
  not? What did you decide?