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旋转与相似三角形动画

旋转与相似三角形动画
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2016-11-13 04:05
测试改名0几何作图
该范例演示了旋转变换在相似三角形中的应用。核心数学概念包括相似三角形的性质和旋转变换。通过使用GeoGebra命令如Rotate、Polygon、Dilate等，可以动态展示旋转前后三角形的相似关系。适合初中及以上学生学习相似三角形的性质和变换。

GeoGebra 命令及参数

  1. Ray(E, L) → l
  2. Point(l) → M
  3. Rotate(M, α, E) → M'
  4. Ray(E, M') → m
  5. Point(y = 0) → A
  6. Segment(A, C) → j
  7. Rotate(C, α, A) → C'
  8. Ray(A, C') → g
  9. Point(g) → D
  10. Segment(A, D) → i
  11. Segment(D, C) → h
  12. Ray(A, C) → f
  13. Angle(C, A, C') → β
  14. Polygon(A, C, D) → poly1, d, a, c
  15. Angle(M, E, M') → γ
  16. Circle(E, i) → e
  17. Circle(E, j) → k
  18. Intersect(k, l, 1) → F
  19. Intersect(e, m, 1) → G
  20. Circle(G, 1) → p
  21. Circle(F, 1) → q
  22. Circle(G, h) → r
  23. Intersect(r, l) → H, U
  24. Dilate(G, b, E) → G'
  25. Dilate(H, b, E) → H'
  26. Segment(G', H') → n
  27. Polygon(E, H', G') → poly2, g', e_1, h'
  28. Angle(poly2) → δ, ε, ζ
  29. Angle(poly1) → η, θ, ι
  30. Segment(E, H') → s
  31. Segment(E, G') → t
  32. Min({j, i, h}) → o
  33. Circle(A, (0.2 * o)) → c_1
  34. Circle(D, (0.2 * o)) → d_1
  35. Circle(C, (0.2 * o)) → f_1
  36. Intersect(c_1, j, 1) → I
  37. Intersect(c_1, i, 1) → J
  38. Intersect(d_1, i, 1) → K
  39. Intersect(d_1, h, 1) → N
  40. Intersect(f_1, h, 1) → O
  41. Intersect(j, xAxis) → P
  42. Intersect(f_1, j, 1) → Q
  43. CircleSector(A, I, J) → g_1
  44. CircleSector(D, K, N) → h_1
  45. CircleSector(C, O, Q) → k_1
  46. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], E) → A'
  47. Vector(A, A') → v
  48. Translate(g_1, v) → p_1
  49. Line(A, t) → i_1
  50. Point(i_1) → R
  51. Angle(D, A, R) → κ
  52. Rotate(p_1, If[1 < u ≤ 2, ((u - 1) * κ), κ], E) → q_1
  53. Dilate(D, If[2 < u ≤ 3, 3 - u, 0], G') → D'
  54. Vector(D, D') → w
  55. Translate(h_1, w) → r_1
  56. Line(D, n) → j_1
  57. Point(j_1) → S
  58. Angle(N, D, S) → λ
  59. Rotate(r_1, If[3 < u ≤ 4, ((u - 3) * λ), λ], G') → s_1
  60. Dilate(C, If[6 < u ≤ 7, 7 - u, 0], H') → C'_1
  61. Vector(C, C'_1) → u_1
  62. Translate(k_1, u_1) → t_1
  63. Line(C, s) → l_1
  64. Point(l_1) → T
  65. Angle(A, C, T) → μ
  66. Rotate(t_1, If[7 < u ≤ 8, ((u - 7) * μ), μ], H') → c_2
  67. CircleArc(A, I, J) → d_2
  68. CircleArc(D, K, N) → e_2
  69. CircleArc(C, O, Q) → f_2