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Pythagorean Triples

Pythagorean Triples. A set of three nonzero whole numbers a, b, and c such that a 2 +b 2 =c 2 . Common Pythagorean Triples are: 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25 Other Pythagorean Triples are multiples of the common (example: 9, 12, 15).

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Pythagorean Triples

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  1. Pythagorean Triples • A set of three nonzero whole numbers a, b, and c such that a2+b2=c2. • Common Pythagorean Triples are: • 3, 4, 5 • 5, 12, 13 • 8, 15, 17 • 7, 24, 25 • Other Pythagorean Triples are multiples of the common (example: 9, 12, 15)

  2. Examples: Are they Pythagorean Triples? Why or why not? • 6, 7, 8 • No, 62+72 does not equal 82 • 10, 24, 26 • Yes, this is a multiple of 5, 12, 13 (times 2) • 8, 25, 26 • No, this is 7, 24, 25 with one added, not multiplied • 4, 7.5, 8.5 • No, there are numbers here that aren’t whole (even though it is a multiple of 8, 15, 17 times one half)

  3. Pythagorean Inequalities • In any triangle ABC, call c the longest side. • If c2<a2+b2, then triangle ABC is acute • If c2>a2+b2, then triangle ABC is obtuse • If c2=a2+b2, then triangle ABC is right • It is important that c be lined up on the LEFT side to compare!!!

  4. Examples: Use Pythagorean Inequalities to determine if the triangle with given sides is acute, right, or obtuse. • 7, 10, 14 • obtuse • 3, 6, 6.5 • acute • 6, 8, 10 • right

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