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梯形与风筝形性质探索

梯形与风筝形性质探索
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2020-03-06 11:00
多边形角向量几何作图滑块动画
①本范例演示梯形与风筝形的几何性质；②涉及核心概念：多边形、角度、向量、几何变换；③作图要点：使用Segment、Line、Point、Angle、Circle、Intersect、Midpoint、Rotate、Ray、Vector等命令构建图形；④适合高中几何教学，用于学生探索和验证图形性质。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Segment(A, C) → g
  3. Line(C, f) → h
  4. Point(h) → D
  5. Segment(B, D) → i
  6. Segment(C, D) → j
  7. Angle(C, A, B) → α
  8. Angle(A, C, D) → β
  9. Angle(C, D, B) → γ
  10. Angle(A, B, D) → δ
  11. Segment(I, J) → r
  12. Segment(I, K) → s
  13. Circle(K, I) → c
  14. Circle(J, I) → d
  15. Intersect(c, d, 2) → L
  16. Segment(J, L) → t
  17. Segment(K, L) → a
  18. Midpoint(g) → M
  19. Midpoint(i) → N
  20. Segment(M, N) → b
  21. Segment(E, F) → k
  22. Line(G, k) → l
  23. Point(l) → O
  24. Segment(E, G) → m
  25. Circle(F, m) → e
  26. Angle(F, E, G) → ε
  27. Rotate(E, (-ε), F) → E'
  28. Angle(E', F, E) → ζ
  29. Rotate(E, ε, F) → E'_1
  30. Angle(E, F, E'_1) → η
  31. Circle(F, m) → p
  32. Segment(F, E'_1) → n
  33. Segment(F, E') → q
  34. Intersect(p, q) → Q,
  35. Segment(G, Q) → g_1
  36. Segment(Q, F) → h_1
  37. Rotate(F, (-ε), E) → F'
  38. Angle(F', E, F) → θ
  39. Ray(F, E') → f_1
  40. Intersect(p, f_1) → P,
  41. Segment(P, F) → i_1
  42. Segment(P, G) → j_1
  43. Angle(F, E, G) → αα
  44. Segment(G, F) → k_1
  45. Segment(E, P) → l_1
  46. Point(b) → H
  47. Point(f) → R
  48. Point(j) → S
  49. Point(l_1) → T
  50. Point(k_1) → U
  51. Vector(E, G) → u
  52. Angle(F, E, G) → κ
  53. Line(G, k) → m_1
  54. Circle(F, m) → c_1
  55. Rotate(E, αα, F) → E'_2
  56. Angle(E, F, E'_2) → ι
  57. Ray(F, E'_2) → n_1
  58. Point(n_1) → V
  59. Intersect(n_1, m_1) → W
  60. Segment(W, F) → p_1
  61. Segment(G, W) → q_1
  62. Segment(E, W) → r_1
  63. Point(r_1) → Z
  64. Point(m) → A_1
  65. Point(i_1) → B_1
  66. Point(p_1) → C_1
  67. Point(r) → D_1
  68. Point(t) → E_1
  69. Point(a) → F_1
  70. Point(s) → G_1
  71. Point(t) → H_1
  72. Segment(K, J) → s_1
  73. Segment(I, L) → t_1
  74. Intersect(s_1, t_1) → I_1
  75. Angle(L, I_1, K) → λ
  76. Angle(K, I, J) → μ
  77. Angle(K, L, J) → ν
  78. Angle(I, K, L) → ξ
  79. Angle(I, J, L) → ο