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Cube, Triangle, and Altitudes

Cube, Triangle, and Altitudes
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2017-07-26 01:11
TriangleSolid GeometryGeometric Construction
This example demonstrates the geometric relationship between a cube, a triangle inside it, and its altitudes. Core math concepts include solid geometry, triangle geometry, and altitude calculation. Construction highlights involve commands like Segment, Line, Intersect, OrthogonalLine, and Angle from GeoGebra. Suitable for high school and above students to understand the connection between spatial and planar geometry.

GeoGebra Commands & Parameters

  1. Segment(A, C) → g
  2. Line(B, g) → j
  3. Segment(A, B) → f
  4. Line(C, f) → i
  5. Intersect(i, j) → E
  6. Segment(C, E) → l
  7. Line(D, l) → n_2
  8. Segment(C, D) → h
  9. Line(B, h) → q
  10. Line(E, h) → m
  11. Intersect(m, n_2) → F
  12. Line(F, g) → c
  13. Intersect(q, c) → H
  14. Segment(A, A + (t1 * (D - A))) → g_1
  15. OrthogonalLine(C, g_1) → j_1
  16. Segment(D, D + (t1 * (H - D))) → i_1
  17. OrthogonalLine(F, i_1) → k_1
  18. Intersect(j_1, k_1) → K
  19. Segment(B, E) → k
  20. Line(A, h) → p
  21. Line(D, g) → r
  22. Intersect(r, p) → G
  23. Segment(A, G) → s
  24. Segment(D, G) → t
  25. Segment(E, F) → a
  26. Segment(F, D) → b
  27. Segment(G, H) → d
  28. Segment(F, H) → e
  29. Segment(H, B) → f_1
  30. Segment(H, H + (t1 * (A - H))) → h_1
  31. Segment(B, B + (t3 * (K - B))) → m_1
  32. Segment(F, F + (t3 * (K - F))) → n_1
  33. Segment(C, C + (t3 * (K - C))) → l_1
  34. Intersect(j_1, g_1) → I
  35. OrthogonalLine(F, i_1) → s_1
  36. Intersect(s_1, i_1) → J
  37. OrthogonalLine(B, h_1) → t_1
  38. Intersect(t_1, h_1) → O
  39. Angle(D, I, C) → α
  40. Angle(H, J, F) → γ
  41. Angle(A, O, B) → β
  42. Segment(C, C + (t2 * (I - C))) → p_1
  43. Segment(F, F + (t2 * (J - F))) → q_1
  44. Segment(B, B + (t2 * (O - B))) → r_1