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Animation 103: Triangle Rotation and Median

Animation 103: Triangle Rotation and Median
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2016-08-21 00:11
TriangleVectorGeometric Construction
In collections Geometry Review Expressing Geometric Properties with Equations (GPE) Cluster
This example demonstrates a rotating triangle animation, focusing on the properties of the median. Key mathematical concepts include triangles, medians, rotation, and angles. Using GeoGebra commands such as Rotate, Line, and Intersect, the dynamic changes in the median during the rotation process are shown. Suitable for middle school and above students to learn geometric transformations and triangle properties.

GeoGebra Commands & Parameters

  1. Circle(A, a_2) → c
  2. Rotate(B, α, A) → B'
  3. Line(A, B') → j
  4. Rotate(j, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → k
  5. Intersect(c, j, 2) → C
  6. OrthogonalLine(C, g) → h
  7. Intersect(g, h) → D
  8. Line(D, j) → i_1
  9. Intersect(k, i_1) → P
  10. Segment(C, D) → l
  11. Segment(A, D) → j_1
  12. Dilate(C, If[0 < b_1 ≤ 1, 1 - b_1, 0], D) → C'
  13. Segment(C, C') → b
  14. Min(b, j_1) → k_2
  15. Circle(D, (0.2 * k_2)) → e
  16. Intersect(e, l, 1) → F
  17. Angle(F, D, P) → δ
  18. Intersect(e, g, 2) → E
  19. CircleSector(D, E, F) → p
  20. Rotate(p, If[2 < b_1 ≤ 3, ((b_1 - 2) * π / 2), π / 2], D) → p'
  21. Angle(B, A, B') → β
  22. Polygon(A, D, C) → poly1, c_1, a_1, d
  23. Point(g) → G
  24. Ray(D, G) → m
  25. Point(m) → H
  26. Ray(D, H) → n
  27. Dilate(D, If[1 < b_1 ≤ 2, 2 - b_1, 0], A) → D'
  28. Segment(D, D') → a
  29. Ray(D, I) → i
  30. Intersect(e, i, 1) → J
  31. CircleSector(D, F, J) → q
  32. Circle(C, (0.2 * k_2)) → r
  33. Circle(A, (0.2 * k_2)) → s
  34. Intersect(s, j_1, 1) → K
  35. Intersect(s, j, 2) → L
  36. Intersect(r, l, 1) → M
  37. Intersect(r, j, 1) → N
  38. CircleSector(C, N, M) → t
  39. CircleSector(A, K, L) → d_1
  40. Rotate(q, If[2 < b_1 ≤ 3, ((-(b_1 - 2)) * π / 2), ((-π)) / 2], D) → q'
  41. CircleSector(C, M, N) → e_1
  42. CircleSector(A, L, K) → f_1
  43. Rotate(A, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → A'
  44. Rotate(D, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → D'_1
  45. Rotate(C, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → C'_1
  46. Polygon(A', D'_1, C'_1) → poly1', c'_1, a', d'_1
  47. Rotate(C, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → C'_2
  48. Rotate(C', If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → C''
  49. Segment(C'_2, C'') → b'
  50. Rotate(D, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → D'_2
  51. Rotate(D', If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → D''
  52. Segment(D'_2, D'') → a'_1
  53. Rotate(d_1, If[4.5 < b_1 ≤ 5.5, ((b_1 - 4.5) * π / 2), π / 2], A) → g_1
  54. CircleArc(A, K, L) → h_1
  55. Rotate(p', If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → p''
  56. Rotate(t, If[5.5 < b_1 ≤ 6.5, ((-(b_1 - 5.5)) * π), (-π)], C) → t'
  57. CircleArc(C, N, M) → k_1
  58. Dilate(C, If[6.5 < b_1 ≤ 7.5, 7.5 - b_1, 0], A) → C'_3
  59. Vector(C, C'_3) → u
  60. Translate(t', u) → t''
  61. Dilate(D, If[9 < b_1 ≤ 10, 10 - b_1, 0], A) → D'_3
  62. Vector(D, D'_3) → v
  63. Rotate(p', If[8 < b_1 ≤ 9, ((b_1 - 8) * δ), δ], D) → p''_1
  64. Translate(p''_1, v) → p_1
  65. Point(k) → O
  66. Rotate(C, If[3.5 < b_1 ≤ 4.5, ((b_1 - 3.5) * π / 2), π / 2], A) → C'_4