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Pythagorean Triples

Pythagorean Triples. Beat the Computer Drill. What are Pythagorean Triples?. Three integers that make the equation a 2 + b 2 = c 2 true are called Pythagorean Triples. The numbers 3, 4 and 5 are a very famous Pythagorean Triple. a 2 + b 2 = c 2. 3 2 + 4 2 = 5 2. 9 + 16 = 25. 4. x.

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Pythagorean Triples

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  1. Pythagorean Triples Beat the Computer Drill

  2. What are Pythagorean Triples? • Three integers that make the equation a2 + b2 = c2 true are called Pythagorean Triples. • The numbers 3, 4 and 5 are a very famous Pythagorean Triple. a2 + b2 = c2 32 + 42 = 52 9 + 16 = 25

  3. 4 x 3 Why Memorize Pythagorean Triples? • Remember how much time it took to figure out 8 x 8 before you memorized it? (8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 = 64) • Think of all the work involved to solve this problem: Wouldn’t it be nice to just know this is 5? a2 + b2 = c2 32 + 42 = x2 9 + 16 = x2 25 = x2 5 = x

  4. Good Pythagorean Triples to Memorize: And multiples of each, like: 3x2, 4x2, 5x2 6 8 10

  5. Directions: • The following slides show common Pythagorean Triples. It is faster to recognize these triples on sight than to apply the Pythagorean Theorem. • When the right triangle appears, SAY ALOUD the length of the missing side. Try to beat the computer by saying the answer BEFORE it appears in 8 seconds.

  6. 4 x 3

  7. 3 4 5 4 5 3

  8. 12 x 5

  9. 5 12 13 12 13 5

  10. 8 10 x

  11. 3 4 5 x 2 x 2 x 2 6 8 10 8 10 6

  12. 50 x 30

  13. 3 4 5 x 10 x 10 x 10 30 40 50 40 50 30

  14. 5 x 3

  15. 3 4 5 4 5 3

  16. 12 13 x

  17. 5 12 13 12 13 5

  18. 24 x 18

  19. 3 4 5 x 6 x 6 x 6 18 24 30 24 30 18

  20. x 8 15

  21. 8 15 17 17 8 15

  22. 0.5 x 0.3

  23. 3 4 5 x .1 x .1 x .1 0.3 0.4 0.5 0.4 0.5 0.3

  24. 36 x 27

  25. 3 4 5 x 9 x 9 x 9 27 36 45 36 45 27

  26. 13 x 5

  27. 5 12 13 12 13 5

  28. 20 25 x

  29. 3 4 5 x 5 x 5 x 5 15 20 25 20 25 15

  30. 17 8 x

  31. 8 15 17 17 8 15

  32. 40 x 24

  33. 3 4 5 x 8 x 8 x 8 24 32 40 32 40 24

  34. 4 5 x

  35. 3 4 5 4 5 3

  36. 15 x 9

  37. 3 4 5 x 3 x 3 x 3 9 16 15 12 15 9

  38. 17 x 15

  39. 8 15 17 17 8 15

  40. 28 35 x

  41. 3 4 5 x 7 x 7 x 7 21 28 35 28 35 21

  42. 16 x 12

  43. 3 4 5 x 4 x 4 x 4 12 16 20 16 20 12

  44. Way to Go!!

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