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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
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The little square in the 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,
3 4 5
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and add them together, 3 4 5
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you get the same number you would get by squaring the other side.
3 4 5
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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.
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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.
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The relationship Pythagorus discovered is now called The Pythagorean Theorem:
b
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The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c,
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then c a b
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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 c a = 15
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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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= 24 10 b 26 (a) (c)
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12 b 15 = 9
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The numbers 3, 4 and 5 are said to form a Pythagorean Triple
Pythagorean Triples There are cases when the lengths of the sides of a right-angled triangle have integral values Whole numbers only (No Fractions) 3 4 5 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 =
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There are an infinite number of Pythagorean triples
5 12 13 There are an infinite number of Pythagorean triples Here are two more examples … 25 7 24
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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)
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