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Rotation and Median Line Animation

Rotation and Median Line Animation
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2017-05-24 22:13
TrianglePolygonTransformationGeometric Construction
This example demonstrates the dynamic behavior of a median line within a triangle during rotation. It involves core concepts like rotation, median line, polygon construction, and geometric transformations. GeoGebra commands such as Rotate, Angle, Segment, Point, Intersect, Circle, Line, and Midpoint are used in the construction. Suitable for high school mathematics education to illustrate the properties of rotational transformations and median lines.

GeoGebra Commands & Parameters

  1. Rotate(A, (a * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Segment(B, A) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Segment(B, C) → h
  7. Segment(A, C) → i
  8. Rotate(A, α / 2, B) → A'_1
  9. Angle(A, B, A'_1) → β
  10. Ray(B, A'_1) → j
  11. Intersect(j, i) → D
  12. Segment(B, D) → k
  13. Min({f, h, k}) → b
  14. Circle(B, (0.25 * b)) → c
  15. Intersect(c, f, 1) → E
  16. Intersect(j, k) → F
  17. Intersect(c, h, 1) → G
  18. Intersect(c, j) → H,
  19. CircleArc(B, E, H) → d
  20. Point(d) → I
  21. Mirror(I, j) → I'
  22. Line(B, I') → l
  23. Line(B, I) → m
  24. Ray(B, I') → n
  25. Ray(B, I) → p
  26. Point(p) → J
  27. Line(A, B) → q
  28. OrthogonalLine(J, q) → r
  29. Intersect(r, q) → K
  30. Point(n) → L
  31. Line(B, C) → s
  32. OrthogonalLine(L, s) → t
  33. Intersect(s, t) → M
  34. OrthogonalLine(L, q) → e
  35. Intersect(q, e) → N
  36. OrthogonalLine(J, s) → f_1
  37. Intersect(s, f_1) → O
  38. Midpoint(J, L) → P
  39. Circle(P, K) → c_1
  40. Polygon(A, C, B) → poly1, b_1, a_1, c_2
  41. CircleSector(B, E, I) → d_1
  42. Angle(I, B, G) → γ
  43. Rotate(d_1, If[0 < o ≤ 1, (o * γ), γ], B) → e_1
  44. Angle(L, M, C) → δ
  45. Angle(K, N, L) → ε
  46. Angle(A, K, J) → ζ
  47. Angle(J, O, C) → η
  48. Dilate(L, If[2 < o ≤ 3, 3 - o, 0], M) → L'
  49. Dilate(L, If[2 < o ≤ 3, 3 - o, 0], N) → L'_1
  50. Segment(L, L') → g_1
  51. Segment(L, L'_1) → h_1
  52. Dilate(J, If[3 < o ≤ 4, 4 - o, 0], O) → J'
  53. Dilate(J, If[3 < o ≤ 4, 4 - o, 0], K) → J'_1
  54. Segment(J, J') → i_1
  55. Segment(J, J'_1) → j_1
  56. Dilate(J, If[4 < o ≤ 5, 5 - o, 0], P) → J'_2
  57. Segment(J, J'_2) → k_1
  58. Dilate(P, If[5 < o ≤ 6, 6 - o, 0], L) → P'
  59. Segment(P, P') → l_1
  60. Rotate(J, If[6 < o ≤ 7, ((o - 6) * π), π], P) → J'_3
  61. Rotate(J'_2, If[6 < o ≤ 7, ((o - 6) * π), π], P) → Q
  62. Segment(J'_3, Q) → m_1
  63. Dilate(P, If[7 < o ≤ 8, 8 - o, 0], N) → P'_1
  64. Segment(P, P'_1) → n_1
  65. Circle(P, P'_1) → p_1

AI Drawing Prompt Reference

Draw a triangle ABC with points A, B, and C as vertices. First, rotate line segment AB around point B, then construct the median AD. Next, use rotations and intersections to create a series of auxiliary line segments and arcs, ultimately forming a dynamically rotating triangle and showing the changes of median AD during the rotation.
The prompt above was compiled from the original drawing commands and is for reference only.