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Puzzle: Combinations of Scalene Triangles

Puzzle: Combinations of Scalene Triangles
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2016-06-09 02:51
TriangleSequenceCoordinate Geometry
This example demonstrates the combinations of scalene triangles. The core mathematical concepts involved include the properties of triangles and combinatorics. Using GeoGebra commands such as Sequence, VerticalText, Point, etc., various combinations of scalene triangles can be constructed. Suitable for middle school and above students to learn geometric construction and combinatorics.

GeoGebra Commands & Parameters

  1. Sequence(Segment[(0, 0 + (2 * k)), (10, 0 + (2 * k))], k, 0, 5) → list2
  2. Sequence(Segment[(0 + (2 * k), 0), (0 + (2 * k), 10)], k, 0, 5) → list1
  3. Sequence(Polygon[(-5, (2 * k)), (0, (2 * k)), (0, 2 + (2 * k)), (-5, 2 + (2 * k))], k, 0, 4) → list3
  4. Sequence(Polygon[((2 * k), 0), ((2 * k) + 2, 0), ((2 * k) + 2, -5), ((2 * k), -5)], k, 0, 4) → list4
  5. VerticalText(text6) → text11
  6. VerticalText(text7) → text12
  7. VerticalText(text8) → text13
  8. VerticalText(text9) → text14
  9. VerticalText(text10) → text15
  10. VerticalText(text47) → text48
  11. VerticalText(text49) → text50
  12. VerticalText(text51) → text52
  13. VerticalText(text53) → text54
  14. VerticalText(text55) → text56
  15. Point(list1) → B1
  16. Point(list1) → C1
  17. Point(list1) → D1
  18. Point(list1) → E1
  19. Point(list3) → F1
  20. Point(list1) → G1
  21. Point(list3) → K1
  22. Point(list1) → L1
  23. Point(list1) → M1
  24. Point(list1) → N1
  25. Point(list1) → O1
  26. Point(list3) → P1
  27. Point(list1) → Q1
  28. Point(list3) → U1
  29. Point(list1) → V1
  30. Point(list1) → Z1
  31. TableText({R1, R2, R3, R4, R5}, "c|_") → Sol
  32. Text(1, A1) → T1
  33. Text(3, A3) → T3
  34. Text(2, A2) → T2
  35. Text(4, A4) → T4
  36. Text(5, A5) → T5
  37. Text(6, A6) → T6
  38. Text(7, A7) → T7
  39. Text(9, A8) → T8
  40. Text(10, A9) → T9
  41. Text(11, A10) → T10
  42. Text(12, A11) → T11
  43. Text(15, A12) → T12
  44. Text(16, A13) → T13
  45. Text(18, A14) → T14
  46. Text(20, A15) → T15
  47. Text(21, A16) → T16
  48. Text(23, A17) → T17
  49. Text(24, A18) → T18
  50. Text(25, A19) → T19
  51. Text(30, A20) → T20
  52. Text(35, A21) → T21
  53. Text(36, A22) → T22
  54. Text(45, A23) → T23
  55. Text(55, A24) → T24
  56. Text(60, A25) → T25