梯形的性质 by Roxana Kim

梯形的性质 by Roxana Kim
几何画板及绘图内容加载中,请稍等……
2017-01-09 10:22
这个范例演示梯形的性质。涉及的核心数学概念包括梯形的定义、性质以及相关几何元素。通过使用GeoGebra命令如Segment、LineBisector、Intersect等,可以动态展示梯形的构造过程。适合初中及以上学生学习几何作图和相关性质。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. LineBisector(a) → b
  3. Intersect(b, a) → C_1
  4. Segment(A, D) → c
  5. Mirror(D, b) → C
  6. Segment(C, B) → d
  7. Segment(C, D) → e
  8. Angle(B, A, D) → α
  9. Angle(A, D, C) → β
  10. Angle(D, C, B) → γ
  11. Angle(C, B, A) → δ
  12. Distance(A, D) → distanceAD
  13. Distance(D, C) → distanceDD'
  14. Distance(C, B) → distanceD'B
  15. Distance(B, A) → distanceBA
  16. Segment(A, C) → i
  17. Segment(B, D) → j
  18. Intersect(i, j) → E_1
  19. Angle(E_1, A, D) → ε
  20. Angle(A, D, E_1) → ζ
  21. Angle(E_1, D, C) → η
  22. Angle(D, C, E_1) → θ
  23. Angle(E_1, C, B) → ι
  24. Angle(C, B, E_1) → κ
  25. Angle(E_1, B, A) → λ
  26. Angle(B, A, E_1) → μ
  27. Distance(A, E_1) → distanceAE
  28. Distance(E_1, C) → distanceED'
  29. Distance(B, E_1) → distanceBE
  30. Distance(E_1, D) → distanceED
  31. Distance(A, C) → distanceAD'
  32. Distance(D, B) → distanceDB
  33. Line(F, G) → p
  34. Line(H, I) → q
  35. OrthogonalLine(H, q) → r
  36. OrthogonalLine(I, q) → s
  37. Point(q) → J
  38. Circle(H, J) → t
  39. Intersect(t, r, 2) → K
  40. CircleArc(H, J, K) → c_1
  41. Point(c_1) → L
  42. Line(L, q) → a_1
  43. Intersect(a_1, s) → M
  44. Segment(L, M) → b_1
  45. Point(b_1) → N
  46. Segment(H, L) → d_1
  47. Segment(L, N) → e_1
  48. Segment(N, I) → f_1
  49. Segment(H, I) → g_1
  50. Angle(N, I, H) → ν
  51. Angle(I, H, L) → ξ
  52. Angle(H, L, N) → ο
  53. Angle(L, N, I) → ρ
  54. Distance(H, L) → distanceHL
  55. Distance(L, N) → distanceLN
  56. Distance(N, I) → distanceNI
  57. Distance(I, H) → distanceIH
  58. Segment(L, I) → h_1
  59. Segment(N, H) → i_1
  60. Intersect(h_1, i_1) → O
  61. Distance(L, O) → distanceLO
  62. Distance(O, N) → distanceON
  63. Distance(O, I) → distanceOI
  64. Distance(O, H) → distanceOH
  65. Distance(L, I) → distanceLI
  66. Distance(N, H) → distanceNH
  67. Angle(L, O, H) → δ_1
  68. Angle(N, O, L) → ε_1
  69. Angle(B, E_1, A) → ζ_1
  70. Angle(B, E_1, C) → η_1
  71. Segment(A, C) → p_1
  72. Segment(D, B) → q_1
  73. Intersect(p_1, q_1) → E
  74. Segment(D, E) → r_1
  75. Segment(C, E) → s_1
  76. Segment(A, E) → t_1
  77. Segment(B, E) → f_2
  78. Segment(L, O) → l
  79. Segment(N, O) → n
  80. Segment(H, O) → j_1
  81. Segment(I, O) → g_2
  82. Segment(H, N) → h_2
  83. Segment(L, I) → i_2
  84. Intersect(h_2, i_2) → P
  85. Angle(P, L, N) → σ
  86. Angle(L, N, P) → τ
  87. Angle(P, N, I) → υ
  88. Angle(N, I, P) → ϕ
  89. Angle(P, I, H) → χ
  90. Angle(I, H, P) → ψ
  91. Angle(P, H, L) → ω
  92. Angle(H, L, P) → α_1

AI 绘图提示语参考

绘制一个梯形ABCD,其中AB和CD是平行的。首先画出AB和CD,然后画出AB的中垂线,找到中垂线与AB的交点C。接着画出AD和DC,通过镜像D关于中垂线得到C'。然后画出AC'和DC',并计算各角和边长。最后,画出辅助线和圆弧,构造出梯形的高和对角线。
以上提示语为根据原始绘图命令整理而来,仅供参考。