构造等腰梯形

构造等腰梯形
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2024-12-17 14:56
本范例演示了如何使用 GeoGebra 构造一个等腰梯形。核心数学概念包括几何作图和多边形的性质。作图要点包括使用圆、线段、旋转和多边形等 GeoGebra 命令。适合的学段或用途包括中小学的几何学科教学。

GeoGebra 命令及参数

  1. Element(randomNumbersC, Mod[questionCount, Length[randomNumbersC]] + 1) → sliderCOriginal
  2. Element(randomNumbersB, Mod[questionCount, Length[randomNumbersB]] + 1) → sliderBOriginal
  3. Element(randomNumbersA, Mod[questionCount, Length[randomNumbersA]] + 1) → sliderAOriginal
  4. Shuffle({1, 2, 3, 4}) → bspList, {1, 2, 4, 3}
  5. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {3, 6, 1, 10, 2, 2, 6, 5, 1, 8}
  6. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  7. Segment(A, B) → segAB
  8. Rotate(B, winkel, A) → B'
  9. Ray(A, B') → g
  10. Polygon((-6, 8), (8, 8), (8, 12), (-6, 12)) → q1, h, i, j, k
  11. Angle(B, A, B') → α
  12. Angle(B, A, B') → alph1
  13. Circle(A, sideD) → c
  14. Point(c) → C
  15. Point(c) → D
  16. Rotate(A, (-winkel), B) → A'
  17. Ray(B, A') → l
  18. Angle(A', B, A) → β
  19. Circle(B, sideD) → e
  20. Point(e) → F
  21. Point(e) → G
  22. CircleArc(B, F, G) → p
  23. Point(e) → S
  24. Point(e) → T
  25. Circle(A, sideB) → p_1
  26. Point(p_1) → U
  27. CircleArc(A, U, V) → q_1
  28. Circle(B, sideB) → r_1
  29. Point(r_1) → W
  30. Point(r_1) → Z
  31. CircleArc(B, W, Z) → s_1
  32. Circle(B, sideD) → t_1
  33. Point(t_1) → A_1
  34. Point(t_1) → B_1
  35. CircleArc(B, A_1, B_1) → c_2
  36. Intersect(If[bsp ≟ 1, s_1, If[bsp ≟ 3, c_2]], l) → H,
  37. Circle(A, sideD) → d_2
  38. Point(d_2) → C_1
  39. Point(d_2) → D_1
  40. CircleArc(A, C_1, D_1) → e_2
  41. Intersect(If[bsp ≟ 3, e_2, If[bsp ≟ 1, q_1]], g) → E,
  42. Segment(E, H) → segCD
  43. Segment(A, E) → segAD
  44. Segment(B, H) → segBC
  45. Angle(A, E, H) → γ
  46. Angle(E, H, B) → δ
  47. Segment(I, J) → segCD2
  48. Rotate(I, winkel, J) → I'
  49. Polygon((-6, 0.5), (9, 0.5), (9, -3), (-6, -3)) → q2, m, n, q, r
  50. Ray(J, I') → s
  51. Angle(I, J, I') → ε
  52. Rotate(J, (-winkel), I) → J'
  53. Ray(I, J') → t
  54. Angle(J', I, J) → ζ
  55. Circle(I, sideD) → c_1
  56. Point(c_1) → K
  57. CircleArc(I, K, L) → d_1
  58. Circle(I, sideB) → f_2
  59. Point(f_2) → G_1
  60. Point(f_2) → H_1
  61. CircleArc(I, G_1, H_1) → g_2
  62. Intersect(If[bsp ≟ 2, d_1, If[bsp ≟ 4, g_2]], t) → M,
  63. Segment(I, M) → segAD2
  64. Circle(J, sideD) → e_1
  65. Point(e_1) → N
  66. Point(e_1) → O
  67. CircleArc(J, N, O) → f_1
  68. Circle(J, sideB) → d
  69. Point(d) → E_1
  70. Point(d) → F_1
  71. CircleArc(J, E_1, F_1) → k_1
  72. Intersect(If[bsp ≟ 2, f_1, If[bsp ≟ 4, k_1]], s) → P,
  73. Segment(J, P) → segBC2
  74. Segment(M, P) → segAB2
  75. Angle(P, M, I) → η
  76. Angle(J, P, M) → θ
  77. Polygon((-6, -4), (-6, 12), (9, 12), (9, -4)) → q3, a, b, g_1, h_1
  78. Segment(A - (0, .12), A + (0, 0.12)) → seg1
  79. Segment(B - (0, .12), B + (0, 0.12)) → seg2
  80. Segment(I - (0, .12), I + (0, 0.12)) → seg3
  81. Segment(J - (0, .12), J + (0, 0.12)) → seg4

AI 绘图提示语参考

画一个等腰梯形,首先绘制一条基线,然后利用旋转和圆的相交构造梯形的非平行边,确保两腰等长,最后连接各顶点形成封闭图形,并标注关键角度。
以上提示语为根据原始绘图命令整理而来,仅供参考。