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动画演示平行四边形与梯形性质

动画演示平行四边形与梯形性质
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2016-06-24 10:12
角解析几何几何作图
①本范例通过动画演示平行四边形与梯形的几何性质，特别是角度、中位线与斜率的关系；②涉及核心数学概念包括角度、梯形、斜率差、中位线、比例、双曲线、正方形等；③作图要点运用了Line, Ray, Point, Midpoint, Slope, OrthogonalLine, Mirror, Dilate, Segment, Circle, Intersect, CircleSector, Vector, Translate, Angle, Rotate, Polygon等GeoGebra命令与对象；④适合高中数学教学，用于理解几何变换与性质。

GeoGebra 命令及参数

  1. Line(A, B) → a
  2. Ray(A, B) → b
  3. Point(b) → C
  4. Midpoint(A, C) → D
  5. Line(A, C) → c
  6. Slope(c) → d
  7. OrthogonalLine(D, c) → g
  8. Point(g) → E
  9. Ray(D, E) → h
  10. Point(h) → F
  11. Slope(h) → i
  12. Line(F, c) → l
  13. Point(l) → G
  14. Point(l) → H
  15. Ray(F, G) → m
  16. Ray(F, H) → n
  17. Point(m) → I
  18. Mirror(I, h) → I'
  19. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'
  20. Segment(A, A') → p
  21. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], I) → A'_1
  22. Segment(A, A'_1) → q
  23. Segment(A, C) → r
  24. Segment(C, I') → s
  25. Segment(I', I) → t
  26. Segment(I, A) → a_1
  27. Circle(A, (0.2 * Min[a_1, r])) → c_1
  28. Circle(I, (0.2 * Min[a_1, r])) → d_1
  29. Intersect(d_1, a_1, 1) → J
  30. Intersect(d_1, t, 1) → K
  31. Intersect(c_1, r, 1) → L
  32. Intersect(c_1, a_1, 1) → M
  33. CircleSector(A, L, M) → e_1
  34. CircleSector(I, J, K) → f_1
  35. Dilate(I, If[2 < o ≤ 3, 3 - o, 0], I') → I'_1
  36. Segment(I, I'_1) → b_1
  37. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], C) → A'_2
  38. Vector(A, A'_2) → u
  39. Translate(A, u) → A'_3
  40. Translate(A'_1, u) → N
  41. Segment(A'_3, N) → q'
  42. OrthogonalLine(A, r) → g_1
  43. Point(g_1) → O
  44. Angle(I, A, O) → α
  45. Angle(I', C, A) → β
  46. Rotate(A'_3, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], C) → P
  47. Rotate(N, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], C) → N'
  48. Segment(P, N') → q''
  49. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], C) → A'_4
  50. Vector(A, A'_4) → v
  51. Translate(e_1, v) → h_1
  52. Rotate(h_1, If[6 < o ≤ 7, ((o - 6) * ((2 * α) + β)), (2 * α) + β], C) → k_1
  53. Dilate(I, If[7 < o ≤ 8, 8 - o, 0], I') → I'_2
  54. Vector(I, I'_2) → w
  55. Translate(f_1, w) → p_1
  56. Rotate(p_1, If[8 < o ≤ 9, ((-(o - 8)) * β), (-β)], I') → q_1
  57. Dilate(A, If[9 < o ≤ 10, 10 - o, 0], I') → A'_5
  58. Segment(A, A'_5) → i_1
  59. Dilate(A, If[10 < o ≤ 11, 11 - o, 0], I) → A'_6
  60. Vector(A, A'_6) → u_1
  61. Translate(A, u_1) → A'_7
  62. Translate(A'_5, u_1) → Q
  63. Segment(A'_7, Q) → j_1
  64. Segment(I, C) → l_1
  65. Angle(L, A, I') → γ
  66. Rotate(A'_7, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], I) → R
  67. Rotate(Q, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], I) → Q'
  68. Segment(R, Q') → m_1
  69. Polygon(A, C, I', I) → poly1, a_2, c_2, i', i_2