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Cuboid with Cross-Sections

Cuboid with Cross-Sections
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2015-09-09 15:16
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates a cuboid with three types of cross-sections: midpoints of parallel edges of the base, diagonals of the base, and diagonals of side faces. It involves core concepts in solid geometry, midpoints, diagonals, and angle calculations. Construction highlights include using commands like Midpoint, Odcinek_3D, If, Segment, and Angle. Suitable for high school geometry teaching and construction practice.

GeoGebra Commands & Parameters

  1. Midpoint(D7, D8) → G
  2. Midpoint(D5, D6) → F
  3. Midpoint(D3, D4) → E
  4. Midpoint(D1, D2) → D
  5. Odcinek_3D(D8, D4, D7, D6) → c, d
  6. Odcinek_3D(D8, D6, D4, D7) → e, f
  7. Odcinek_3D(D8, D7, D6, D4) → g, h
  8. Odcinek_3D(D7, D3, D5, D8) → i, j
  9. Odcinek_3D(D7, D5, D8, D3) → k, l
  10. Odcinek_3D(D5, D1, D6, D7) → m, n_1
  11. Odcinek_3D(D5, D6, D7, D1) → p, q
  12. Odcinek_3D(D6, D2, D8, D5) → s, t
  13. Odcinek_3D(D2, D1, D4, D6) → a_1, b_1
  14. Odcinek_3D(D2, D4, D6, D1) → c_1, d_1
  15. Odcinek_3D(D1, D3, D2, D5) → e_1, f_1
  16. Odcinek_3D(D3, D4, D1, D7) → g_1, h_1
  17. If(n ≟ 1 ∧ p_1, Polygon[D, E, G, F]) → wielokąt1
  18. If(n ≟ 2 ∧ p_1, Polygon[D1, D4, D8, D5]) → wielokąt2
  19. If(n ≟ 3 ∧ p_1, Polygon[D1, D2, D8, D7]) → wielokąt3
  20. Segment(D, F) → i_1
  21. Segment(E, G) → j_1
  22. Segment(D, E) → k_1
  23. Segment(F, G) → l_1
  24. Segment(F, E) → m_1
  25. Angle(G, F, E) → γ
  26. Angle(F, E, G) → δ
  27. Midpoint(D1, D4) → B
  28. Midpoint(D5, D8) → C
  29. Segment(B, C) → s_1
  30. Segment(D1, D4) → t_1
  31. Segment(D5, D8) → a_2
  32. Segment(D5, D4) → b_2
  33. Angle(D8, D5, D4) → ε
  34. Angle(D5, D4, D8) → ζ
  35. Segment(D1, D8) → c_2
  36. Segment(D2, D8) → e_2
  37. Segment(D1, D7) → f_2
  38. Angle(D2, D8, D6) → η
  39. Angle(D6, D2, D8) → θ
  40. Angle(D7, D8, D1) → ι
  41. Angle(D7, D1, D8) → κ