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Triangle Centers and Exploration

Triangle Centers and Exploration
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2016-04-19 05:40
TriangleCoordinate GeometryGeometric Construction
In collections Besondere Punkte/Special Points
This example demonstrates the geometric properties of triangles, including the centroid, orthocenter, incenter, and circumcenter. Using GeoGebra commands such as Polygon, Midpoint, Line, etc., dynamic exploration of the triangle's center points and their properties is possible. Suitable for middle school and above students to learn geometric construction and related concepts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Midpoint(b) → D
  3. Midpoint(a) → E
  4. Midpoint(c) → F
  5. Line(B, D) → d
  6. Line(E, A) → e
  7. Line(C, F) → f
  8. Intersect(d, e) → Centroid
  9. OrthogonalLine(B, b) → g
  10. OrthogonalLine(C, c) → h
  11. OrthogonalLine(A, a) → i
  12. Intersect(g, h) → Orthocentre
  13. AngularBisector(A, B, C) → j
  14. AngularBisector(C, A, B) → k
  15. AngularBisector(B, C, A) → l
  16. Intersect(j, k) → Incentre
  17. LineBisector(c) → m
  18. LineBisector(b) → n
  19. LineBisector(a) → p
  20. Intersect(m, n) → Circumcentre
  21. OrthogonalLine(Incentre, a) → q
  22. Intersect(q, a) → K
  23. Circle(Incentre, K) → r
  24. Circle(Circumcentre, B) → s
  25. Line(Orthocentre, Centroid) → a_1
  26. Circle(Circumcentre, C) → c_1
  27. OrthogonalLine(Incentre, a) → b_1
  28. Intersect(b_1, a) → G
  29. Circle(Incentre, G) → d_1
  30. Line(C, Centroid) → f_1
  31. Intersect(g, b) → H
  32. Angle(C, H, B) → α
  33. Intersect(i, a) → I
  34. Intersect(h, c) → J
  35. Angle(A, J, C) → β
  36. Angle(B, I, Orthocentre) → γ
  37. Angle(A, F, Circumcentre) → δ
  38. Angle(C, D, Circumcentre) → ε
  39. Angle(B, E, Circumcentre) → ζ
  40. Angle(B, C, Incentre) → η
  41. Angle(Incentre, C, A) → θ
  42. Circle(E, D, F) → k_1
  43. Segment(F, E) → m_1
  44. Segment(F, D) → n_1
  45. LineBisector(n_1) → p_1
  46. LineBisector(m_1) → q_1
  47. Intersect(p_1, q_1) → L
  48. Midpoint(Orthocentre, B) → M
  49. Midpoint(Orthocentre, C) → N
  50. Midpoint(Orthocentre, A) → O
  51. Segment(P, A) → r_1
  52. Segment(P, C) → s_1
  53. Segment(P, B) → t_1
  54. Angle(B, P, A) → ι
  55. Angle(A, P, C) → κ
  56. Angle(C, P, B) → λ
  57. LaTeX(μ, true, true) → text4
  58. LaTeX(ι, true, true) → text5
  59. LaTeX(κ, true, true) → text6
  60. LaTeX(λ, true, true) → text7
  61. AngularBisector(c, a) → a_2, b_2
  62. AngularBisector(c, b) → c_2, d_2
  63. AngularBisector(b, a) → e_2, f_2
  64. Intersect(a_2, c_2) → Q
  65. Intersect(c_2, e_2) → R
  66. Intersect(a_2, e_2) → S
  67. OrthogonalLine(Q, c) → g_2
  68. OrthogonalLine(S, a) → h_2
  69. OrthogonalLine(R, b) → i_2
  70. Intersect(g_2, c) → T
  71. Intersect(h_2, a) → U
  72. Intersect(i_2, b) → V
  73. Circle(R, V) → k_2
  74. Circle(Q, T) → p_2
  75. Circle(S, U) → q_2
  76. Line(A, B) → j_2
  77. Line(C, A) → l_2
  78. Line(B, C) → m_2