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Howe Truss

Howe Truss
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2017-05-13 02:30
TriangleCoordinate GeometryGeometric Construction
In collections Geometry Activities - Timber Truss Structures
This example demonstrates the construction of a Howe Truss, a common bridge structure. The key mathematical concepts include the properties of triangles and geometric construction. Using commands such as rotation, line, and segment, the structure of a Howe Truss can be built. Suitable for middle school and above students to learn geometric construction and bridge structures.

GeoGebra Commands & Parameters

  1. Rotate(A_2, 120°, B_2) → A'_1
  2. Line(B_2, A_2) → f_2
  3. Line(B_2, A'_1) → g_2
  4. Line(A_2, A'_1) → h_2
  5. Segment(A_2, B_2) → i_2
  6. Segment(B_2, A'_1) → j_2
  7. Segment(A'_1, A_2) → k_2
  8. OrthogonalLine(B_2, k_2) → a_2
  9. Rotate(A_2, 30°, B_2) → A_1
  10. Line(B_2, A_1) → f_1
  11. Rotate(A'_1, (-(30°)), B_2) → E_1
  12. Line(B_2, E_1) → j_1
  13. Midpoint(k_2) → A
  14. LineBisector(A_2, A'_1) → f
  15. Segment(A, B_2) → g
  16. Rotate(A'_1, 30°, A) → B
  17. Rotate(A_2, (-(30°)), A) → C
  18. Line(A, C) → h
  19. Line(A, B) → i
  20. Intersect(h, i_2) → D
  21. Intersect(i, j_2) → E
  22. Segment(A, D) → j
  23. Segment(A, E) → k
  24. OrthogonalLine(D, k_2) → l
  25. OrthogonalLine(E, k_2) → m
  26. Intersect(l, k_2) → F
  27. Intersect(m, k_2) → I
  28. Segment(F, D) → n
  29. Segment(I, E) → p
  30. Angle(D, F, A_2) → α
  31. Angle(A'_1, I, E) → β
  32. Angle(D, B_2, A) → γ
  33. Angle(A, B_2, E) → δ
  34. Angle(A, D, B_2) → ε
  35. Angle(B_2, E, A) → ζ
  36. Angle(B_2, A, D) → η
  37. Angle(E, A, B_2) → θ

AI Drawing Prompt Reference

Draw a Howe Truss structure by first rotating point A2 120 degrees around point B2 to get A'_1, then draw line f_2 connecting B2 and A2, line g_2 connecting B2 and A'_1, and line h_2 connecting A2 and A'_1. Next, draw segment i_2 between A2 and B2, segment j_2 between A'_1 and B2, and segment k_2 between A2 and A'_1. Then, find the midpoint A of k_2 and draw the angle bisector f of A2 and A'_1, followed by segment g between A and B2. Rotate A'_1 30 degrees around A to get E_1, and draw line j_1 between B2 and E_1. Continue constructing other key points and segments as described until the entire Howe Truss structure is completed.
The prompt above was compiled from the original drawing commands and is for reference only.