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Converse of Pythagorean Theorem and Triples

a^2 b^2 = c^2

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Converse of Pythagorean Theorem and Triples

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  1. Tuesday WELCOMEBACK! Quarter 4 starts today!

  2. Name- _______________________________ Warm-Up Date-________________________________Quarter 4 Directions: Circle the correct word to make the sentence true. • The hypotenuse is the longest/shortestside in a right triangle. • A triangle with the side lengths 4,5,and 6is/is not a right triangle because 42 + 52 is equal/not equalto 62 . Directions: Write T for True and F for False on the line for #3-5. 3. ______ The hypotenuse of a right triangle can be any one of the three sides. 4. ______ One leg of the triangle at the right has a length of 9 cm. 5. ______ The hypotenuse of the triangle at the right has a length of 15 cm 6. Write the formula for the Pythagorean Theorem: ____________________________. 7. The bottom of a 17-foot ladder is placed on level ground 8 feet from the side of a house as shown in the figure below. Find the vertical height at which the top of the ladder touches the side of the house.

  3. The hypotenuse is the longest/shortest side in a right triangle. • A triangle with the side lengths 4,5,and 6 is/is not a right triangle because 42 + 52 is equal/not equalto 62 . 3. F The hypotenuse of a right triangle can be any one of the three sides. 4. T One leg of the triangle at the right has a length of 9 cm. 5. T The hypotenuse of the triangle at the right has a length of 15 cm 6. Write the formula for the Pythagorean Theorem:. a2 + b2 = c2 7. The bottom of a 17-foot ladder is placed on level ground 8 feet from the side of a house as shown in the figure below. Find the vertical height at which the top of the ladder touches the side of the house. The vertical height at which the top of the ladder touches the side of the house is 15 feet. • Answer Key a2 + b2 = c2 82 + b2 = 172 64 + b2 = 289 -64 -64 b2 = 225 √ b2 = √225 b = 15

  4. Teacher notes

  5. Teacher notes

  6. Can you find any patterns in the following chart of numbers?

  7. Work with your table/partners try to figure out the missing side measurements.

  8. Do you see any patterns?

  9. Pythagorean Triples

  10. Pythagorean Triples

  11. Pythagorean Triples

  12. Pythagorean Triples

  13. Pythagorean Triples

  14. Pythagorean Triples

  15. Pythagorean Triples

  16. Now choose two of the triples on the chart and scale them to create more triples. Be prepared to show your work to the class.

  17. Now sort out the cards into 2 categories: No, it is a Right triangle Yes, it is not a Right triangle

  18. Is it a right triangle? 6, 8, 10

  19. Is it a right triangle? 6, 8, 10

  20. Is it a right triangle? 15, 20, 25

  21. Is it a right triangle? 15, 20, 25

  22. Is it a right triangle? 10, 17, 19

  23. Is it a right triangle? 10, 17, 19

  24. Is it a right triangle? 8, 25, 29

  25. Is it a right triangle? 8, 25, 29

  26. Is it a right triangle? 15, 36, 39

  27. Is it a right triangle? 15, 36, 39

  28. Is it a right triangle? 18, 20, 22

  29. Is it a right triangle? 18, 20, 22

  30. Is it a right triangle? 6,7,8

  31. Is it a right triangle? 6,7,8

  32. Is it a right triangle? 14,48, 50

  33. Is it a right triangle? 14,48, 50

  34. Is it a right triangle? 12,15 ,18

  35. Is it a right triangle? 12,15 ,18

  36. Is it a right triangle? 5,12,13

  37. Is it a right triangle? 5,12,13

  38. Is it a right triangle? 7,24 ,25

  39. Is it a right triangle? 7,24 ,25

  40. Is it a right triangle? 8,15 ,17

  41. Is it a right triangle? 8,15 ,17

  42. Is it a right triangle? 6,9 12,

  43. Is it a right triangle? 6,9 12,

  44. Is it a right triangle? 10,13,16,

  45. Is it a right triangle? 10,13, 16,

  46. Converse of the Pythagorean Theorem

  47. Click here to view video. Start at 11:37

  48. Here is a visual for you to see it better.

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