矩形的性质 by David T

矩形的性质 by David T
几何画板及绘图内容加载中,请稍等……
2013-06-21 07:47
这个范例演示了矩形的性质,包括对角线相等、对边平行且相等等。涉及的核心数学概念有平行线、对角线性质、角度等。通过使用GeoGebra命令如Line、Segment、Polygon等进行构造。适合初中及以上学生学习几何作图。

GeoGebra 命令及参数

  1. Line(A, B) → e_1
  2. OrthogonalLine(A, e_1) → i
  3. Segment(A, B) → d_1
  4. Point(i) → D
  5. Polygon(A, D, B) → P, a, b, d
  6. Midpoint(D, B) → E
  7. Rotate(A, (-rotateΔ), E) → A'
  8. Rotate(D, (-rotateΔ), E) → D'
  9. Rotate(B, (-rotateΔ), E) → B'
  10. Polygon(A', D', B') → P', c, e, f
  11. OrthogonalLine(B, e_1) → f_3
  12. Intersect(f_3, e_1) → F
  13. Midpoint(B', A') → G
  14. If(rotateΔ > 0°, G) → K
  15. Midpoint(d_1) → M
  16. Angle(B', A', D') → γ
  17. Angle(B, A, D) → δ
  18. Angle(D, B, A) → ζ
  19. Angle(D', B', A') → α
  20. Angle(A, D, B) → β
  21. Angle(A', D', B') → ε
  22. Segment(D', A') → c_1
  23. Segment(A, D) → a_1
  24. Segment(B', A') → f_1
  25. Segment(A, D) → a_2
  26. Segment(D', A') → c_2
  27. Segment(B', A') → f_2
  28. Segment(A, B) → d_2
  29. Segment(D, E) → g
  30. Segment(B, E) → g_1
  31. Segment(A, E) → h
  32. Segment(A', E) → h_1
  33. Angle(E, A, D) → η
  34. Angle(B, A, E) → θ
  35. Angle(D, A', E) → ι
  36. Angle(E, A', B) → κ
  37. Angle(A, D, A') → λ
  38. Angle(A', B, A) → μ
  39. Line(E, e_1) → j
  40. Line(E, f_3) → k
  41. Point(j) → L
  42. Point(j) → N
  43. Point(k) → O
  44. Point(k) → Q
  45. Segment(O, Q) → l
  46. Segment(L, N) → m
  47. Polygon(A, D, A', B) → P''', a_3, d_3, a', b_1
  48. Rotate(A, (-turn), E) → A'_1
  49. Rotate(D, (-turn), E) → D'_1
  50. Rotate(A', (-turn), E) → A''
  51. Rotate(B, (-turn), E) → B'_1
  52. Polygon(A'_1, D'_1, A'', B'_1) → poly1, a'_1, d'_1, a'', b'_1
  53. Polygon(A, D, A', B) → polyfold, a_4, d_4, a'_2, b_2
  54. PointIn(polyfold) → drag
  55. LineBisector(drag, A') → n
  56. Intersect(d_4, n) → H
  57. Intersect(n, a'_2) → I
  58. Intersect(n, a_4) → J
  59. Intersect(n, b_2) → R
  60. Polygon(H, drag, I) → poly2, i_1, h_2, c_3
  61. OrthogonalLine(drag, h_2) → p
  62. Line(J, h_2) → q
  63. Intersect(p, q) → S
  64. Polygon(drag, I, J, S) → poly3, c_4, i_2, j_1, s
  65. OrthogonalLine(drag, i_1) → r
  66. Line(R, i_1) → t
  67. Intersect(r, t) → T
  68. Polygon(drag, H, R, T) → poly4, c_5, h_3, r_1, t_1

AI 绘图提示语参考

绘制一个矩形ABCD,确保对角线相等且平行。首先画出AB线段,然后画出AB的垂线,确定点D。接着画出矩形ABCD,找到对角线中点E,绕E点旋转矩形180度得到A'B'C'D'。连接B'和A',并画出B'和A'的中点G。测量并标记所有角度,确保对边平行且对角相等。
以上提示语为根据原始绘图命令整理而来,仅供参考。