Download - 7-2 Pythagorean Theorem Intro
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a
b
c
222 cba =+
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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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The little square
90o
in theangle tells you it is aright angle.
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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,
3
4
5
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and you square the lengths of the two sides that make up the right angle,
24233
4
5
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and add them together,
3
4
5
2423 22 43 +
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22 43 +
you get the same number you would get by squaring the other side.
222 543 =+3
4
5
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Is that correct?
222 543 =+ ?
25169 =+ ?
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It is. And it is true for any right triangle.
8
6
10222 1086 =+
1006436 =+
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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
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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
a
b
is called the
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And the length of the hypotenuse
is usually labeled c.
a
b
c
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The relationship Pythagorus discovered is now called The Pythagorean Theorem:
a
b
c
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The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c,
a
b
c
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then
a
b
c
.222 cba =+
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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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482
Using The Pythagorean Theorem,
48
36c
362+ = c2
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Why? Can you see that we have a right triangle?
48
36c
482 362+ = c2
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Which side is the hypotenuse? Which sides are the legs?
48
36c
482 362+ = c2
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=+ 22 3648
Then all we need to do is calculate:
=+12962304
=3600 2c
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And you end up 60 miles from where you started.
48
3660
So, since c2 is 3600, c is 60.So, since c2 is 3600, c is
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Find the length of a diagonal of the rectangle:
15"
8"?
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Find the length of a diagonal of the rectangle:
15"
8"?
b = 8
a = 15
c
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222 cba =+ 222 815 c=+ 264225 c=+ 2892 =c 17=c
b = 8
a = 15
c
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Find the length of a diagonal of the rectangle:
15"
8"17
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Practice using The Pythagorean Theorem to solve these right triangles:
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5
12
c = 13
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10
b
26
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10
b
26
= 24
(a)
(c)
222 cba =+222 2610 =+ b
676100 2 =+ b1006762 −=b
5762 =b24=b
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12
b
15
= 9