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任意梯形中通过交点的平行线段关系

任意梯形中通过交点的平行线段关系
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2017-09-08 09:50
多边形向量解析几何变换几何作图
该范例演示了任意梯形中通过交点的平行线段与梯形底边的关系。核心数学概念包括几何作图和变换。使用了Ray, Point, Segment, Dilate, Midpoint, Line, OrthogonalLine, Angle, Vector, Translate, Circle, Intersect, Rotate, Slope, Polygon等GeoGebra命令。适合初中及以上学生学习梯形性质和几何变换。

GeoGebra 命令及参数

  1. Ray(A, B) → b
  2. Point(b) → C
  3. Segment(A, C) → r
  4. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'
  5. Segment(A, A') → p
  6. Midpoint(A, C) → D
  7. Line(A, C) → c
  8. OrthogonalLine(D, c) → g
  9. Point(g) → E
  10. Ray(D, E) → h
  11. Point(h) → F
  12. Line(F, c) → l
  13. Point(l) → G
  14. Ray(F, G) → m
  15. Point(m) → I
  16. Angle(C, A, I) → δ
  17. Dilate(A, If[6 < o ≤ 7, 7 - o, 0], I) → A'_6
  18. Vector(A, A'_6) → u_1
  19. Translate(A, u_1) → A'_7
  20. Segment(I, A) → a_1
  21. Circle(A, (0.2 * Min[a_1, r])) → c_1
  22. Intersect(c_1, r, 1) → L
  23. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], I) → A'_1
  24. Segment(A, A'_1) → q
  25. Ray(I, F) → f_2
  26. Point(f_2) → I'
  27. Angle(L, A, I') → γ
  28. Rotate(A'_7, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], I) → R
  29. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], I') → A'_5
  30. Translate(A'_5, u_1) → Q
  31. Rotate(Q, If[7 < o ≤ 8, (((-(o - 7)) * 2) * γ), (-2 * γ)], I) → Q'
  32. Line(A, B) → a
  33. Slope(c) → d
  34. Slope(h) → i
  35. Point(l) → H
  36. Ray(F, H) → n
  37. Segment(C, I') → s
  38. Segment(I', I) → t
  39. Intersect(c_1, a_1, 1) → M
  40. Dilate(I, If[2 < o ≤ 3, 3 - o, 0], I') → I'_1
  41. Segment(I, I'_1) → b_1
  42. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], C) → A'_2
  43. Vector(A, A'_2) → u
  44. Translate(A, u) → A'_3
  45. Translate(A'_1, u) → N
  46. OrthogonalLine(A, r) → g_1
  47. Point(g_1) → O
  48. Angle(I, A, O) → α
  49. Angle(I', C, A) → β
  50. Rotate(A'_3, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], C) → P
  51. Rotate(N, If[4 < o ≤ 5, (((-(o - 4)) * 2) * α), (-2 * α)], C) → N'
  52. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], C) → A'_4
  53. Vector(A, A'_4) → v
  54. Dilate(I, If[7 < o ≤ 8, 8 - o, 0], I') → I'_2
  55. Vector(I, I'_2) → w
  56. Segment(I, C) → l_1
  57. Polygon(A, C, I', I) → poly1, a_2, c_2, i', i_2
  58. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], I') → C'
  59. Segment(C, C') → f_1
  60. Segment(A, I) → h_1
  61. Segment(A, C) → i_1
  62. Segment(C, I') → j_1
  63. Segment(I', I) → k_1
  64. Min({h_1, i_1, j_1, k_1}) → e_1
  65. Circle(A, (0.2 * e_1)) → p_1
  66. Intersect(p_1, i_1) → J,
  67. Rotate(J, If[4 < o ≤ 5, ((o - 4) * δ), δ], A) → J'
  68. CircleSector(A, J, J') → d_1
  69. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], I) → A'_8
  70. Vector(A, A'_8) → v_1
  71. Translate(d_1, v_1) → q_1
  72. Line(A, I) → m_1
  73. Circle(I, 2) → r_1
  74. Intersect(r_1, m_1, 2) → K
  75. Ray(I, K) → n_1
  76. Segment(A, I') → s_1
  77. Segment(I, C) → t_1
  78. Intersect(s_1, t_1) → S
  79. Line(S, p) → g_2
  80. Intersect(m_1, g_2) → T
  81. Line(I', C) → h_2
  82. Intersect(h_2, g_2) → U
  83. Dilate(A, If[6 < o ≤ 7, 7 - o, 0], I') → A'_9
  84. Segment(A, A'_9) → j_2
  85. Dilate(C, If[7 < o ≤ 8, 8 - o, 0], S) → C'_1
  86. Segment(C, C'_1) → k_2
  87. Dilate(S, If[8 < o ≤ 9, 9 - o, 0], I) → S'
  88. Segment(S, S') → l_2
  89. Dilate(S, If[9 < o ≤ 10, 10 - o, 0], T) → S'_1
  90. Segment(S, S'_1) → m_2
  91. Dilate(I, If[10 < o ≤ 11, 11 - o, 0], T) → I'_3
  92. Vector(I, I'_3) → w_1
  93. Translate(q_1, w_1) → d_2
  94. Dilate(S, If[9 < o ≤ 10, 10 - o, 0], U) → S'_2
  95. Segment(S, S'_2) → n_2
  96. Rotate(S, If[11 < o ≤ 12, ((o - 11) * π), π], S) → S'_3
  97. Rotate(S'_1, If[11 < o ≤ 12, ((o - 11) * π), π], S) → V
  98. Segment(S'_3, V) → p_2