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Dynamic Triangle Theorem Demo

Dynamic Triangle Theorem Demo
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2017-01-12 03:11
TriangleAngleVectorGeometric ConstructionSlider Animation
This example dynamically demonstrates a neat, not-often-seen theorem about a triangle with a 60-degree angle. It involves core math concepts like angles, exponents, congruence, LCM and GCD, 2D vectors, and fractal geometry. Construction highlights include commands like Rotate, Angle, Ray, Point, Polygon, Line, Segment, Min, Circle, Intersect, CircleSector, and Dilate in GeoGebra. Suitable for high school and above learners exploring geometric theorems and dynamic properties.

GeoGebra Commands & Parameters

  1. Rotate(A, 60°, B) → A'
  2. Angle(A, B, A') → α
  3. Ray(B, A) → f
  4. Ray(B, A') → g
  5. Point(f) → C
  6. Point(g) → D
  7. Polygon(C, D, B) → poly1, b, c, d
  8. Rotate(D, 60°, B) → D'
  9. Angle(D, B, D') → β
  10. Rotate(C, (-(60°)), B) → C'
  11. Angle(C', B, C) → γ
  12. Line(C', D') → h
  13. Segment(B, C) → i
  14. Segment(B, D) → j
  15. Min(i, j) → a
  16. Segment(C, D) → k
  17. Min(i, k) → l
  18. Min(a, l) → m
  19. Circle(B, (0.2 * m)) → e
  20. Intersect(e, h, 1) → E
  21. Intersect(e, i, 1) → F
  22. Intersect(e, j, 1) → G
  23. Intersect(e, h, 2) → H
  24. Angle(D, C, B) → δ
  25. Angle(B, D, C) → ε
  26. Rotate(D, δ / 2, C) → D'_1
  27. Angle(D, C, D'_1) → ζ
  28. Ray(C, D'_1) → p
  29. Rotate(B, ε / 2, D) → B'
  30. Angle(B, D, B') → η
  31. Ray(D, B') → q
  32. Circle(C, (0.2 * m)) → r
  33. Circle(D, (0.2 * m)) → s
  34. Intersect(r, p, 1) → I
  35. Intersect(r, k, 1) → J
  36. Intersect(s, j, 1) → K
  37. Intersect(s, q, 1) → L
  38. Intersect(i, q) → M
  39. Intersect(j, p) → N
  40. CircleSector(B, E, F) → t
  41. Rotate(t, If[0 < n ≤ 1, (n * π / 3), π / 3], B) → t'
  42. Rotate(t', If[2 < n ≤ 3, ((n - 2) * π / 3), π / 3], B) → t''
  43. Rotate(t'', If[4 < n ≤ 5, ((-(n - 4)) * π / 3), ((-π)) / 3], B) → t'''
  44. Dilate(C, If[5 < n ≤ 6, 6 - n, 0], N) → C'_1
  45. Segment(C, C'_1) → f_1
  46. Dilate(D, If[6 < n ≤ 7, 7 - n, 0], M) → D'_2
  47. Segment(D, D'_2) → g_1
  48. Intersect(r, i, 1) → O
  49. Intersect(s, k, 1) → P
  50. CircleSector(C, I, O) → c_1
  51. CircleSector(D, L, P) → d_1
  52. Rotate(c_1, If[7 < n ≤ 8, ((-(n - 7)) * ζ), (-ζ)], C) → e_1
  53. Rotate(d_1, If[8 < n ≤ 9, ((-(n - 8)) * η), (-η)], D) → h_1
  54. Dilate(C, If[9 < n ≤ 10, 10 - n, 0], M) → C'_2
  55. Segment(C, C'_2) → i_1
  56. Dilate(D, If[10 < n ≤ 11, 11 - n, 0], N) → D'_3
  57. Segment(D, D'_3) → j_1
  58. Rotate(C, If[11 < n ≤ 12, ((-(n - 11)) * δ), (-δ)], C) → C'_3
  59. Rotate(C'_2, If[11 < n ≤ 12, ((-(n - 11)) * δ), (-δ)], C) → Q
  60. Segment(C'_3, Q) → k_1
  61. Rotate(M, If[11 < n ≤ 12, ((-(n - 11)) * δ), (-δ)], C) → M'
  62. Rotate(D, If[12 < n ≤ 13, ((n - 12) * ε), ε], D) → D'_4
  63. Rotate(D'_3, If[12 < n ≤ 13, ((n - 12) * ε), ε], D) → R
  64. Segment(D'_4, R) → l_1

AI Drawing Prompt Reference

Draw a triangle with a 60-degree angle and dynamically demonstrate a related theorem. Start from vertex B, draw two rays BC and BD at 60 degrees, meeting at points C and D. Draw a circle centered at B, intersecting rays BC and BD at points F and G. Connect CF and DG, and find their intersections with the circle at points E and H. Draw two smaller circles centered at C and D, intersecting rays CF and DG at points I and J. Finally, draw a sector centered at B, connecting E and F, with dynamically changing angle.
The prompt above was compiled from the original drawing commands and is for reference only.