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Triangular Pyramid Construction Example

Triangular Pyramid Construction Example
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2013-11-30 21:27
Solid GeometryTransformationGeometric Construction
This is an example for teachers to demonstrate the construction of a triangular pyramid. It involves basic geometric concepts of a triangular pyramid such as vertices, base, and edges. Using GeoGebra commands like Translate, Mirror, Vector, etc., the construction process can be dynamically shown. Suitable for math education from middle school and above.

GeoGebra Commands & Parameters

  1. Translate(O, Vector[u * x_0]) → O'_1
  2. Translate(O, Vector[u * y_0]) → O'_2
  3. Translate(O, Vector[u * z_0]) → O'_3
  4. Mirror(O'_1, O) → G
  5. Translate(O, Vector[-0.1 * u * z_0]) → O'_5
  6. Translate(O, Vector[-u * y_0]) → O'
  7. Vector(O', O'_2) → v
  8. Vector(G, O'_1) → w
  9. Vector(O'_5, O'_3) → z
  10. Segment(O', O'_2) → c
  11. Segment(O'_1, G) → d
  12. Line(O, O'_3) → i
  13. Sequence(O + i * y_0, i, -u, u) → liste5
  14. Sequence(O + i * x_0, i, -u, u) → liste1
  15. Sequence(O + i * z_0, i, -u + 8, u) → liste3
  16. RotateText("\copyright uStas\;\;Strelets", 90*°) → надпись24
  17. Отрезок3D(S, A, C, B) → e, f
  18. Отрезок3D(S, C, B, A) → g, j
  19. Отрезок3D(S, B, A, C) → k, l
  20. Отрезок3D(B, A, S, C) → m, n
  21. Отрезок3D(C, B, S, A) → p, q
  22. Отрезок3D(A, C, S, B) → r, s
  23. Segment(S, O_1) → t
  24. Polygon(А, В, С) → многоугольник1, c_2, a_2, b_2
  25. Circle(А, В, С) → c_1
  26. LineBisector(А, С) → a_1
  27. LineBisector(С, В) → b_1
  28. Intersect(b_1, a_1) → I_2
  29. AngularBisector(В, А, С) → d_1
  30. AngularBisector(А, В, С) → e_1
  31. Intersect(e_1, d_1) → J_3
  32. OrthogonalLine(J_3, c_2) → f_1
  33. Intersect(c_2, f_1) → K
  34. Circle(J_3, K) → g_1
  35. Point(w) → M
  36. Point(w) → L
  37. Point(v) → N
  38. Point(v) → P
  39. Line(P, d) → h_1
  40. Line(N, d) → i_1
  41. Line(M, c) → j_1
  42. Line(L, c) → k_1
  43. Intersect(h_1, j_1) → D
  44. Intersect(i_1, j_1) → E
  45. Intersect(k_1, i_1) → F
  46. Intersect(h_1, k_1) → H
  47. Polygon(D, E, F, H) → многоугольник2, d_2, e_2, f_2, h_2
  48. Polygon(B, A, C) → многоугольник3, c_3, b_3, a_3
  49. Point(c_1) → V
  50. Point(c_1) → W
  51. Conic(J_1, B, A, I_1, C) → p_1
  52. Intersect(g_1, b_2) → O_3,
  53. Intersect(g_1, a_2) → Q,
  54. Point(g_1) → R
  55. Point(g_1) → T
  56. Conic(U, Z, B_1, C_1, D_1) → q_1
  57. Area(А, В, С) → l_1
  58. Segment(B_1, J) → n_1
  59. Segment(J, U) → r_1
  60. Segment(J, C_1) → s_1
  61. Segment(J_3, K) → t_1
  62. Segment(O_3, J_3) → g_2
  63. Segment(J_3, Q) → i_2
  64. Segment(I_2, С) → j_2
  65. Segment(А, I_2) → k_2
  66. Segment(I_2, В) → l_2
  67. Segment(A, I) → n_2
  68. Segment(I, C) → p_2
  69. Segment(I, B) → q_2
  70. Distance(А, В) → расстояниеАВ
  71. Distance(А, В) → b
  72. Distance(В, С) → w_1
  73. Distance(А, С) → a
  74. Area(А, В, С) → z_1
  75. Angle(В, А, С) → γ
  76. Angle(С, В, А) → δ
  77. Angle(А, С, В) → ε
  78. Segment(A, S) → s_2
  79. Segment(S, C) → t_2
  80. Segment(S, B) → d_3
  81. Segment(A, B) → e_3
  82. Segment(B, C) → f_3
  83. Segment(A, C) → g_3
  84. Distance(А, O_2) → j_3
  85. Distance(В, O_2) → l_3
  86. Distance(С, O_2) → n_3

AI Drawing Prompt Reference

Draw a triangular pyramid with base triangle ABC and apex S. First, create the base triangle ABC, then construct the three edges SA, SB, and SC from point S to the sides of the base triangle to form the triangular pyramid. Next, use the sides of the base triangle to construct auxiliary lines and angle bisectors to determine the position of point S.
The prompt above was compiled from the original drawing commands and is for reference only.