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Triangle Center

Triangle Center
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2019-03-27 16:36
TriangleCoordinate GeometryGeometric Construction
This example demonstrates how to construct the center of a triangle using GeoGebra, covering core concepts in coordinate geometry and geometric construction. Key GeoGebra commands and objects used include Polygon, LineBisector, Intersect, OrthogonalLine, AngularBisector, Midpoint, Line, Circle, Center, and Segment. Suitable for high school mathematics education or geometric learning to understand triangle properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. LineBisector(b) → f
  3. LineBisector(a) → g
  4. LineBisector(c) → h
  5. Intersect(f, h) → O
  6. OrthogonalLine(A, a) → i
  7. OrthogonalLine(B, b) → j
  8. OrthogonalLine(C, c) → k
  9. Intersect(i, j) → H
  10. AngularBisector(A, B, C) → l
  11. AngularBisector(B, C, A) → m
  12. AngularBisector(C, A, B) → n
  13. Intersect(l, m) → I_1
  14. Midpoint(A, C) → M_3
  15. Midpoint(B, C) → M_2
  16. Midpoint(A, B) → M_1
  17. Line(B, M_3) → p
  18. Line(C, M_1) → q
  19. Line(A, M_2) → r
  20. Intersect(p, q) → G
  21. Polygon(B, C, 3) → poly1, s, t, d, J
  22. Polygon(A, B, 3) → poly2, e, f_1, g_1, K
  23. Polygon(C, A, 3) → poly3, h_1, i_1, j_1, L
  24. Circle(K, A, B) → c_1
  25. Circle(J, B, C) → d_1
  26. Circle(A, C, L) → e_1
  27. Intersect(c_1, d_1, 2) → F
  28. Circle(M_1, M_2, M_3) → k_1
  29. Center(k_1) → N
  30. OrthogonalLine(I_1, c) → l_1
  31. Intersect(l_1, c) → D
  32. Circle(I_1, D) → p_1
  33. Intersect(p_1, k_1) → F_4, , ,
  34. Circle(B, A, C) → q_1
  35. Line(O, H) → E
  36. Segment(I_1, A) → m_1
  37. OrthogonalLine(A, m_1) → n_1
  38. Segment(I_1, C) → r_1
  39. OrthogonalLine(C, r_1) → s_1
  40. Intersect(m_1, r_1) → I
  41. Intersect(n_1, s_1) → P
  42. Segment(I, B) → t_1
  43. OrthogonalLine(B, t_1) → a_1
  44. Intersect(n_1, a_1) → Q
  45. Intersect(s_1, a_1) → R
  46. OrthogonalLine(Q, c) → b_1
  47. OrthogonalLine(R, a) → f_2
  48. OrthogonalLine(P, b) → g_2
  49. Intersect(b_1, c) → S
  50. Intersect(f_2, a) → T
  51. Intersect(g_2, b) → U
  52. Circle(Q, S) → c_2
  53. Circle(R, T) → d_2
  54. Circle(P, U) → e_2
  55. Line(H, O) → h_2
  56. Line(B, A) → i_2
  57. Line(B, C) → j_2
  58. Line(A, C) → k_2
  59. Intersect(j_2, a) → V
  60. Intersect(j_2, a) → W
  61. Intersect(j_2, a) → Z
  62. Intersect(j_2, a) → A_1
  63. Intersect(i_2, c) → B_1
  64. Intersect(i_2, c) → C_1
  65. Intersect(i_2, c) → D_1
  66. Intersect(i_2, c) → E_1
  67. Intersect(i_2, c) → F_5
  68. Intersect(i_2, c) → G_1
  69. Intersect(c_2, i_2) → H_1, T_C
  70. Intersect(k_2, b) → J_1
  71. Intersect(e_2, k_2) → T_B,
  72. Intersect(d_2, j_2) → T_A,
  73. Segment(T_A, A) → l_2
  74. Segment(C, T_C) → m_2
  75. Segment(B, T_B) → n_2
  76. Intersect(l_2, m_2) → K_1
  77. Intersect(c_2, k_1) → F_1, , ,
  78. Intersect(d_2, k_1) → F_2, , ,
  79. Intersect(e_2, k_1) → F_3, , ,