正方形的性质 by David T

正方形的性质 by David T
几何画板及绘图内容加载中,请稍等……
2013-06-21 07:49
这个范例演示了正方形的性质,包括对角线相等且互相垂直、边长相等、内角均为90度等。涉及的核心数学概念有几何作图、线段、角度、旋转等。通过使用GeoGebra命令如Circle、Line、OrthogonalLine、Segment、Intersect、Polygon、Midpoint、Rotate等,可以动态展示正方形的性质。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. Circle(A, B) → p
  2. Line(A, B) → e_1
  3. OrthogonalLine(A, e_1) → i
  4. Segment(A, B) → d_1
  5. Intersect(p, i) → D, C
  6. Polygon(A, D, B) → P, a, b, d
  7. Midpoint(D, B) → E
  8. Rotate(A, (-rotateΔ), E) → A'
  9. Rotate(D, (-rotateΔ), E) → D'
  10. Rotate(B, (-rotateΔ), E) → B'
  11. Polygon(A', D', B') → P', c, e, f
  12. OrthogonalLine(B, e_1) → f_3
  13. Intersect(f_3, e_1) → F
  14. Midpoint(B', A') → G
  15. If(rotateΔ > 0°, G) → K
  16. Midpoint(d_1) → M
  17. Angle(B', A', D') → γ
  18. Angle(B, A, D) → δ
  19. Angle(D, B, A) → ζ
  20. Angle(D', B', A') → α
  21. Angle(A, D, B) → β
  22. Angle(A', D', B') → ε
  23. Segment(D', A') → c_1
  24. Segment(A, D) → a_1
  25. Segment(B', A') → f_1
  26. Segment(A, D) → a_2
  27. Segment(D', A') → c_2
  28. Segment(B', A') → f_2
  29. Segment(A, B) → d_2
  30. Segment(D, E) → g
  31. Segment(B, E) → g_1
  32. Segment(A, E) → h
  33. Segment(A', E) → h_1
  34. Angle(E, A, D) → η
  35. Angle(B, A, E) → θ
  36. Angle(D, A', E) → ι
  37. Angle(E, A', B) → κ
  38. Angle(A, D, A') → λ
  39. Angle(A', B, A) → μ
  40. Line(E, e_1) → j
  41. Line(E, f_3) → k
  42. Point(j) → L
  43. Point(j) → N
  44. Point(k) → O
  45. Point(k) → Q
  46. Segment(O, Q) → l
  47. Segment(L, N) → m
  48. Intersect(p, i, 2) → I
  49. Line(A, E) → q
  50. Point(q) → H
  51. Point(q) → J
  52. Segment(H, J) → s
  53. Polygon(A, D, A', B) → P'', a_3, d_3, a', b_1
  54. Rotate(A, turn, E) → A'_1
  55. Rotate(D, turn, E) → D'_1
  56. Rotate(A', turn, E) → A''
  57. Rotate(B, turn, E) → B'_1
  58. Rotate(A, (-turn), E) → A'_2
  59. Rotate(D, (-turn), E) → D'_2
  60. Rotate(A', (-turn), E) → A''_1
  61. Rotate(B, (-turn), E) → B'_2
  62. Polygon(A'_2, D'_2, A''_1, B'_2) → P''', a'_2, d'_2, a''_1, b'_2
  63. Angle(D, E, A) → ν
  64. Line(E, D) → n
  65. Point(n) → R
  66. Point(n) → S
  67. Segment(R, S) → r
  68. Polygon(A, D, A', B) → polyfold, a_4, d_4, a'_1, b_2
  69. LineBisector(drag, A') → t
  70. Intersect(t, f) → U
  71. Intersect(c, a'_1) → V
  72. Intersect(t, c) → W
  73. Polygon(U, drag, W) → poly1, w, u, t_1
  74. Intersect(t, a) → Z
  75. OrthogonalLine(drag, u) → i_1
  76. Line(Z, u) → j_1
  77. Intersect(i_1, j_1) → A_1
  78. Polygon(W, drag, A_1, Z) → poly2, w_1, t_2, a_5, z
  79. OrthogonalLine(drag, w) → k_1
  80. Intersect(t, d) → B_1
  81. Line(B_1, w) → l_1
  82. Intersect(k_1, l_1) → C_1
  83. Polygon(U, drag, C_1, B_1) → poly3, u_1, t_3, c_3, b_3
  84. LineBisector(peel, B) → m_1
  85. Intersect(m_1, c) → D_1
  86. Intersect(m_1, d) → E_1
  87. Polygon(peel, E_1, D_1) → poly4, d_5, t_4, e_2
  88. Intersect(f, d_4) → F_1
  89. Intersect(m_1, f) → G_1
  90. OrthogonalLine(peel, d_5) → n_1
  91. Line(G_1, d_5) → p_1
  92. Intersect(n_1, p_1) → H_1
  93. Polygon(peel, E_1, G_1, H_1) → poly5, t_5, e_3, g_2, h_2
  94. Intersect(m_1, a) → I_1
  95. OrthogonalLine(peel, e_2) → q_1
  96. Line(I_1, e_2) → r_1
  97. Intersect(r_1, q_1) → J_1
  98. Polygon(peel, D_1, I_1, J_1) → poly6, t_6, d_6, i_2, j_2

AI 绘图提示语参考

绘制一个正方形,包括其对角线、边和角度。首先画一个圆和一条线,然后构造正方形的两条对角线,接着画正方形的边并旋转正方形,最后标注所有角度并确保对角线相等且垂直。
以上提示语为根据原始绘图命令整理而来,仅供参考。