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Fan Truss Model

Fan Truss Model
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2017-05-13 02:27
TriangleAngleTransformationGeometric Construction
In collections Geometry Activities - Timber Truss Structures
This example demonstrates the geometric construction and properties of a fan truss. It involves core math concepts like geometric construction, angle measurement, line intersection, and rotational symmetry. Key GeoGebra commands and objects used include Rotate, Line, Segment, OrthogonalLine, Intersect, and Angle, as outlined in the construction summary. Suitable for high school students or teachers to understand truss structures, geometric transformations, and spatial relationships.

GeoGebra Commands & Parameters

  1. Rotate(A_1, 120°, B_1) → A'_1
  2. Line(B_1, A_1) → f_1
  3. Line(B_1, A'_1) → g_1
  4. Line(A_1, A'_1) → h_1
  5. Segment(A_1, B_1) → i_1
  6. Segment(B_1, A'_1) → j_1
  7. Segment(A'_1, A_1) → k_1
  8. OrthogonalLine(B_1, k_1) → a_1
  9. Rotate(A_1, 30°, B_1) → A
  10. Line(B_1, A) → f
  11. Intersect(f, k_1) → B
  12. Rotate(A'_1, 100°, B) → C
  13. Line(B, C) → g
  14. Intersect(g, i_1) → D
  15. Segment(B, D) → h
  16. Angle(B, D, B_1) → β
  17. Segment(B, B_1) → i
  18. Rotate(A'_1, (-(30°)), B_1) → E
  19. Line(B_1, E) → j
  20. Intersect(j, k_1) → F
  21. Segment(B_1, F) → k
  22. Rotate(A_1, (-(100°)), F) → I
  23. Line(F, I) → l
  24. Intersect(l, j_1) → J
  25. Segment(F, J) → m
  26. Angle(B_1, J, F) → ε
  27. Rotate(A'_1, 40°, F) → K
  28. Rotate(A_1, (-(40°)), B) → L
  29. Line(L, B) → n
  30. Line(F, K) → p
  31. Angle(F, B, B_1) → θ
  32. Angle(B_1, F, B) → ι
  33. Angle(B, B_1, F) → η
  34. Rotate(A_1, (-(30°)), B) → O
  35. Angle(O, B, A_1) → κ
  36. Rotate(A'_1, 30°, F) → P
  37. Angle(A'_1, F, P) → λ
  38. Line(B, O) → q
  39. Line(F, P) → r
  40. Intersect(q, i_1) → M
  41. Intersect(r, j_1) → N
  42. Segment(B, M) → s
  43. Segment(F, N) → t
  44. Angle(B, A_1, M) → α
  45. Angle(N, A'_1, F) → γ

AI Drawing Prompt Reference

Draw a fan truss model with three vertices A, A', and B, and their segments and angles. Start by rotating A 120 degrees around B to get A', then draw line segments BA and BA', and their perpendicular line a and symmetric line A'. Next, rotate A 30 degrees around B to get A, draw line segment BF and find its intersection with segment i to get point B, and continue in this manner to find other key points C, D, E, F, I, J, K, L, M, N. Finally, draw all segments and angles to form the complete fan truss model.
The prompt above was compiled from the original drawing commands and is for reference only.