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等腰与不等边三角形动态演示

等腰与不等边三角形动态演示
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2018-02-06 09:25
测试改名0圆三角函数几何作图滑块动画
①本范例动态演示等腰与不等边三角形的几何性质与面积计算；②涉及核心概念：等腰三角形、不等边三角形、面积、有理数、三角函数、菱形；③构造要点：使用 GeoGebra 命令如 Circle（圆）、Intersect（交点）、Dilate（缩放）、Rotate（旋转）、Polygon（多边形）等；④适合高中数学教学，用于理解几何变换与计算。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Intersect(c, q) → O, P
  3. CircleArc(A, O, P) → d
  4. Point(d) → C
  5. Midpoint(C, A) → W
  6. Circle(W, 3) → t_1
  7. CircleArc(A, C, P) → e
  8. Point(e) → D
  9. Midpoint(C, D) → Q
  10. Midpoint(Q, A) → R
  11. Line(R, D) → n
  12. OrthogonalLine(Q, n) → s
  13. Intersect(n, s) → S
  14. Dilate(C, If[9 < j ≤ 10, 10 - j, 0], S) → C'_2
  15. Segment(C, C'_2) → m_1
  16. Line(W, m_1) → b_1
  17. Point(b_1) → A_1
  18. Dilate(D, If[7 < j ≤ 8, 8 - j, 0], R) → D'
  19. Segment(D, D') → g_1
  20. Line(W, g_1) → n_1
  21. Intersect(t_1, n_1, 2) → Z
  22. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], C) → A'
  23. Segment(A, A') → a
  24. Angle(C, A, D) → α
  25. Rotate(A, If[1 < j ≤ 2, ((j - 1) * α), α], A) → A'_1
  26. Rotate(A', If[1 < j ≤ 2, ((j - 1) * α), α], A) → A''
  27. Segment(A'_1, A'') → a'
  28. Segment(A, C) → b
  29. Segment(C, D) → f
  30. Segment(D, A) → g
  31. Midpoint(f) → E
  32. Segment(A, E) → h
  33. Midpoint(h) → F
  34. Segment(A, F) → i
  35. Segment(F, E) → k
  36. Circle(A, (0.35 * i)) → p
  37. Circle(E, (0.15 * Distance[D, E])) → r
  38. Intersect(r, f, 2) → G
  39. Intersect(r, h, 1) → H
  40. Intersect(r, f, 1) → I
  41. Intersect(p, b, 1) → J
  42. Intersect(p, h, 1) → K
  43. Intersect(p, g, 1) → L
  44. Circle(A, B) → c_1
  45. Dilate(C, If[2 < j ≤ 3, 3 - j, 0], D) → C'
  46. Segment(C, C') → l
  47. Polygon(C, D, A) → poly1, a_1, c_2, d_1
  48. Circle(C, (0.2 * Distance[D, E])) → e_1
  49. Intersect(e_1, b) → M,
  50. Intersect(e_1, f) → N,
  51. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], F) → A'_2
  52. Dilate(F, If[5 < j ≤ 6, 6 - j, 0], E) → F'
  53. Dilate(E, If[6 < j ≤ 7, 7 - j, 0], D) → E'
  54. Rotate(E, If[7 < j ≤ 8, ((j - 7) * π), 3.141592653589793], E) → E'_1
  55. Rotate(E', If[7 < j ≤ 8, ((j - 7) * π), 3.141592653589793], E) → E''
  56. Dilate(C, If[9 < j ≤ 10, 10 - j, 0], D) → C'_1
  57. Vector(C, C'_1) → u
  58. Angle(E, C, A) → β
  59. CircleArc(A, C, A'') → s_1
  60. Line(A, Q) → m
  61. Angle(S, C, A) → γ
  62. Intersect(n, a) → T
  63. Angle(T, D, C) → δ
  64. Dilate(A, If[4 < j ≤ 5, 5 - j, 0], R) → A'_3
  65. Segment(A, A'_3) → t
  66. Dilate(R, If[5 < j ≤ 6, 6 - j, 0], Q) → R'
  67. Segment(R, R') → f_1
  68. Rotate(A, If[6 < j ≤ 7, ((j - 6) * π), π], R) → A'_4
  69. Rotate(A'_3, If[6 < j ≤ 7, ((j - 6) * π), π], R) → U
  70. Segment(A'_4, U) → t'
  71. Segment(D, S) → h_1
  72. Circle(D, (0.3 * h_1)) → k_1
  73. Circle(C, (0.3 * h_1)) → p_1
  74. Ray(C, S) → i_1
  75. Ray(C, A) → j_1
  76. Intersect(p_1, j_1) → V,
  77. Dilate(Q, If[8 < j ≤ 9, 9 - j, 0], S) → Q'
  78. Segment(Q, Q') → l_1
  79. Angle(D, S, Q) → ε
  80. Rotate(V, If[11 < j ≤ 12, ((-(j - 11)) * γ), (-γ)], C) → V'
  81. CircleSector(C, V', V) → q_1
  82. Dilate(C, If[12 < j ≤ 13, 13 - j, 0], W) → C'_3
  83. Vector(C, C'_3) → v
  84. Angle(A_1, W, Z) → ζ
  85. Translate(q_1, v) → r_1
  86. Rotate(r_1, If[13 < j ≤ 14, ((j - 13) * ζ), ζ], W) → d_2
  87. Dilate(W, If[14 < j ≤ 15, 15 - j, 0], D) → W'
  88. Vector(W, W') → w
  89. Translate(d_2, w) → e_2