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Triangular Pyramid Geometric Constructor for Teachers

Triangular Pyramid Geometric Constructor for Teachers
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2015-10-13 06:49
TriangleAngleVectorSolid GeometryGeometric Construction
This example demonstrates how to construct a triangular pyramid (tetrahedron) in three-dimensional space using GeoGebra. The core mathematical concepts include solid geometry (volume calculation of pyramids), application of the Pythagorean theorem in 3D space, and geometric relationships between polygons and angles. Construction highlights: Use the Polygon command to create the triangular base, apply Отрезок3D for 3D edges, implement Vector and Mirror for translation and reflection transformations, utilize LineBisector, AngularBisector, and OrthogonalLine for angle bisectors and perpendicular lines, and employ Distance and Area commands for measurements. This example is ideal for middle and high school mathematics teachers to demonstrate solid geometry concepts, and serves as a valuable learning resource for students studying spatial vectors and 3D coordinate geometry, particularly suitable for teaching pyramid properties, geometric proofs, and GeoGebra 3D construction techniques.

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