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Pythagorean Triples

Pythagorean Triples. What you should know…. What’s the Pythagorean Theorem?. What do you know already? What are the important parts? How does it work?. So how does the Pythagorean Theorem work?. ???. 9 ft. 12 ft. What if you’re missing a leg?. ???. 24 cm. 26 cm.

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Pythagorean Triples

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  1. Pythagorean Triples What you should know…

  2. What’s the Pythagorean Theorem? • What do you know already? • What are the important parts? • How does it work?

  3. So how does the Pythagorean Theorem work? ??? 9 ft 12 ft

  4. What if you’re missing a leg? ??? 24 cm 26 cm

  5. Multiple Ways to find an answer • Draw Squares (fun) • Formula (algebra) • Recognize a Pythagorean Triple! No work involved!

  6. What is a Pythagorean Triple? • A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule: a2+ b2 = c2 • The smallest, most common triple is 3, 4, 5. • Let’s see it in action…

  7. Triples • Here is a list of the 5 smallest triples… • (3,4,5) (5,12,13) (7,24,25) (8,15,17) (9,40,41) • If you can learn these, there will be multiple problems you won’t have to work out…ever!

  8. Scale • You can get a new triple by using one you already know… • For example, we know that 3, 4, 5 is a Pythagorean Triple… • If we multiply each of those numbers by 2, we have a 6, 8, 10…is 6, 8, 10 a triple?

  9. Scale • So, using your list of triples… • What about a triangle with 25, 60, 65? Is that based on a triple?

  10. Use scale and Pythagorean Triples to determine the missing measure 20 in 12 in ????

  11. You Try… Use your list… Use your list… • What’s the length of the hypotenuse with legs of 10 and 24? • What’s the length of the missing leg of a right triangle with one leg of 21 and a hypotenuse of 75?

  12. So… • Memorize at least the first few triples and you’ll save yourself a ton of work! 

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