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Special Right Triangles

Special Right Triangles. Take a square…. Find its diagonal. Here it is. We’ll let each of the sides of the square be “x”. They are all equal. d. x. x. Look at your formula sheets. You will need to get into the habit of using these for special right triangles.

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Special Right Triangles

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  1. Special Right Triangles

  2. Take a square…

  3. Find its diagonal Here it is

  4. We’ll let each of the sides of the square be “x”. They are all equal. d x x

  5. Look at your formula sheets. You will need to get into the habit of using these for special right triangles. 45o-45o-90o x√2 x x

  6. Summarize the pattern:

  7. 45o-45o-90o leg leg leg

  8. 45o-45o-90o 6 6 6

  9. Practice:

  10. 45o-45o-90o 8 8 8

  11. 45o-45o-90o 5 5 5

  12. 45o-45o-90o 10 10 10

  13. 45o-45o-90o 2

  14. 45o-45o-90o

  15. 45o- 45o-90o

  16. 45o-45o-90o

  17. Now Let’s take an Equilateral Triangle…

  18. … Find its Altitude

  19. See how the altitude halved the side. x x a x

  20. Now, lets look at half this triangle, turned on its altitude. x x x a a

  21. Summarize the pattern:

  22. 30o-60o-90o Shorter Leg Hypotenuse Longer leg

  23. 30o-60o-90o ½ Hyp. Hyp. ½ Hyp.

  24. 30o-60o-90o

  25. Practice:

  26. 30o-60o-90o

  27. 30o-60o-90o

  28. 30o-60o-90o

  29. 30o-60o-90o

  30. 30o-60o-90o

  31. 30o-60o-90o

  32. 30o-60o-90o

  33. 30o-60o-90o

  34. 30o-60o-90o

  35. 30o-60o-90o

  36. Review Both Patterns:

  37. 45o-45o-90o leg leg leg

  38. 30o-60o-90o ½ Hyp. Hyp. ½ Hyp.

  39. Mixed Practice:

  40. 8 8 8

  41. 10 10 10

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