MathPlotAI Logo MathPlotAI

Quadrilateral Mystery

Quadrilateral Mystery
Loading the math board and drawing, please wait…
2016-09-24 09:41
PolygonAngleTransformation
This example demonstrates an interesting yet uncommon property of quadrilaterals. It involves core geometric concepts such as angles and rotations. Using GeoGebra commands like Polygon, Angle, Rotate, Ray, Intersect, etc., you can dynamically explore the properties of quadrilaterals. Suitable for middle school and above students or teachers to understand geometric transformations and quadrilateral properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Angle(B, A, D) → α
  3. Angle(A, D, C) → β
  4. Angle(D, C, B) → γ
  5. Angle(C, B, A) → δ
  6. Rotate(B, α / 2, A) → B'
  7. Angle(B, A, B') → ε
  8. Ray(A, B') → f
  9. Rotate(A, β / 2, D) → A'
  10. Angle(A, D, A') → ζ
  11. Ray(D, A') → g
  12. Rotate(D, γ / 2, C) → D'
  13. Angle(D, C, D') → η
  14. Ray(C, D') → h
  15. Rotate(C, δ / 2, B) → C'
  16. Angle(C, B, C') → θ
  17. Ray(B, C') → i
  18. Intersect(h, i) → F
  19. Intersect(f, i) → E
  20. Intersect(f, g) → H
  21. Intersect(g, h) → G
  22. Circle(G, F, E) → e
  23. Line(E, G) → j
  24. Line(H, F) → k
  25. Midpoint(D, C) → I
  26. Midpoint(B, C) → J
  27. Midpoint(A, B) → K
  28. Midpoint(A, D) → L
  29. Line(D, C) → l
  30. Line(C, B) → m
  31. Line(B, A) → n
  32. Line(A, D) → p
  33. Intersect(p, m) → M
  34. Intersect(n, l) → N
  35. Min({a, b, c, d}) → o
  36. Circle(A, (0.25 * o)) → r
  37. Circle(B, (0.25 * o)) → q
  38. Circle(D, (0.25 * o)) → s
  39. Circle(C, (0.25 * o)) → t
  40. Intersect(q, m, 1) → O
  41. Intersect(q, i, 1) → P
  42. Intersect(r, n, 1) → Q
  43. Intersect(r, f, 1) → R
  44. Intersect(s, p, 1) → S
  45. Intersect(s, g, 1) → T
  46. Intersect(t, l, 1) → U
  47. Intersect(t, h, 1) → V
  48. CircleSector(A, Q, R) → c_1
  49. CircleSector(C, U, V) → d_1
  50. CircleSector(B, O, P) → e_1
  51. CircleSector(D, S, T) → f_1
  52. Dilate(B, If[0 < u ≤ 1, 1 - u, 0], F) → B'_1
  53. Dilate(C, If[0 < u ≤ 1, 1 - u, 0], F) → C'_1
  54. Segment(B, B'_1) → g_1
  55. Segment(C, C'_1) → h_1
  56. Dilate(D, If[1 < u ≤ 2, 2 - u, 0], H) → D'_1
  57. Segment(D, D'_1) → i_1
  58. Dilate(A, If[1 < u ≤ 2, 2 - u, 0], H) → A'_1
  59. Segment(A, A'_1) → j_1
  60. Rotate(e_1, If[2 < u ≤ 3, ((u - 2) * θ), θ], B) → k_1
  61. Rotate(d_1, If[3 < u ≤ 4, ((u - 3) * η), η], C) → p_1
  62. Rotate(f_1, If[4 < u ≤ 5, ((u - 4) * ζ), ζ], D) → q_1
  63. Rotate(c_1, If[5 < u ≤ 6, ((u - 5) * ε), ε], A) → r_1
  64. Center(e) → W
  65. Rotate(E, If[7.5 < u ≤ 8.5, (((u - 7.5) * 2) * π), (2 * π)], W) → E'
  66. CircleArc(W, E, E') → s_1