MathPlotAI Logo MathPlotAI

Morley's Trisector Theorem Demonstration

Morley's Trisector Theorem Demonstration
Loading the math board and drawing, please wait…
2022-06-28 20:39
TriangleAngleGeometric Construction
This example demonstrates Morley's Trisector Theorem, which states that the intersection points of the angle trisectors of any triangle form an equilateral triangle. The core mathematical concepts involved include angles, triangles, geometric construction, rotation, and intersection points. The construction utilizes GeoGebra commands/objects such as Segment, Angle, AngularBisector, Intersect, Rotate, Ray, and Polygon. It is suitable for high school and above students to understand the proof process and construction methods of classic geometric theorems.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Angle(B, A, C) → a
  5. Angle(B, C, A) → b
  6. Angle(A, B, C) → c
  7. AngularBisector(h, f) → i, j
  8. AngularBisector(g, h) → k, l
  9. AngularBisector(g, f) → m, n
  10. AngularBisector(B, C, A) → p
  11. Intersect(p, f) → D
  12. Rotate(D, b1, C) → D'
  13. Rotate(D, (-b1), C) → D'_{1}
  14. Ray(C, D'_{1}) → q
  15. Ray(C, D') → r
  16. AngularBisector(C, B, A) → s
  17. Intersect(s, h) → E
  18. Rotate(E, c1, B) → E'
  19. Rotate(E, (-c1), B) → E'_{1}
  20. Ray(B, E'_{1}) → t
  21. Ray(B, E') → d
  22. Intersect(q, d) → F
  23. AngularBisector(B, A, C) → e
  24. Intersect(e, g) → G
  25. Rotate(G, a1, A) → G'
  26. Rotate(G, (-a1), A) → G'_{1}
  27. Ray(A, G') → f_1
  28. Ray(A, G'_{1}) → g_1
  29. Intersect(g_1, r) → H
  30. Intersect(t, f_1) → I
  31. Polygon(F, I, H) → t1, h_1, f_2, i_1
  32. Segment(B, F) → j_1
  33. Segment(B, I) → k_1
  34. Segment(C, F) → l_1
  35. Segment(H, C) → m_1
  36. Segment(I, A) → n_1
  37. Segment(A, H) → p_1
  38. Angle(C, B, F) → α
  39. Angle(F, B, I) → β
  40. Angle(I, B, A) → γ
  41. Angle(B, C, F) → δ
  42. Angle(F, C, H) → ε
  43. Angle(H, C, A) → ζ
  44. Angle(B, A, I) → η
  45. Angle(I, A, H) → θ
  46. Angle(H, A, C) → ι

AI Drawing Prompt Reference

Draw a triangle ABC, then trisect each angle and connect the intersection points of the trisectors to form a new triangle DEF. Next, rotate these intersection points and connect the new intersection points GHI to form an equilateral triangle.
The prompt above was compiled from the original drawing commands and is for reference only.