平行四边形的几何作图 by Melissa Patti

平行四边形的几何作图 by Melissa Patti
几何画板及绘图内容加载中,请稍等……
2015-10-30 08:44
这个范例演示了如何使用GeoGebra构造平行四边形。核心数学概念包括平行线、距离、旋转等。通过使用Polygon、Segment、Rotate等命令,可以动态地展示平行四边形的性质。适合初中及以上学生学习几何变换和基本的几何作图。

GeoGebra 命令及参数

  1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
  2. Segment(E, F) → e
  3. OrthogonalLine(E, e) → f
  4. OrthogonalLine(F, e) → g
  5. Point(f) → G
  6. Point(g) → H
  7. OrthogonalLine(G, f) → h
  8. OrthogonalLine(H, h) → i
  9. Intersect(g, h) → I
  10. Polygon(E, G, I, F) → poly2, e_1, g_1, i_1, f_1
  11. Segment(J, K) → j
  12. Segment(L, M) → k
  13. Line(N, k) → l
  14. Line(M, k) → m
  15. Segment(L, N) → n
  16. Line(M, n) → p
  17. Intersect(l, p) → O
  18. Polygon(M, L, N, O) → poly3, m_1, l_1, n_1, o
  19. Segment(J, P) → q
  20. Segment(K, Q) → r
  21. Segment(P, Q) → s
  22. Polygon(J, K, Q, P) → poly4, j_1, k_1, q_1, p_1
  23. Segment(R, S) → t
  24. Rotate(R, 40*°, R) → R'
  25. Rotate(S, 40*°, R) → S'
  26. Segment(R', S') → t'
  27. Rotate(R', 140*°, S') → R''
  28. Rotate(S', 140*°, S') → S''
  29. Segment(R'', S'') → t''
  30. Segment(S, R'') → a_1
  31. Polygon(R, S, R'', S') → poly5, r_1, s_1, r'', s'
  32. Segment(T, U) → b_1
  33. LineBisector(b_1) → c_1
  34. Point(c_1) → V
  35. Segment(T, V) → d_1
  36. Line(U, d_1) → h_1
  37. Segment(V, U) → t_1
  38. Line(T, t_1) → a_2
  39. Intersect(c_1, h_1) → W
  40. Polygon(T, W, U, V) → poly6, t_2, w, u, v
  41. Angle(B, A, D) → α
  42. Angle(A, D, C) → β
  43. Angle(D, C, B) → γ
  44. Angle(C, B, A) → δ
  45. Distance(A, C) → distanceAC
  46. Segment(A, C) → b_2
  47. Segment(D, B) → c_2
  48. Distance(D, B) → distanceDB
  49. Angle(F, E, G) → ε
  50. Angle(E, G, I) → ζ
  51. Angle(G, I, F) → η
  52. Angle(I, F, E) → θ
  53. Segment(E, I) → d_2
  54. Segment(G, F) → e_2
  55. Distance(E, I) → distanceEI
  56. Distance(G, F) → distanceGF
  57. Angle(V, T, W) → ι
  58. Angle(T, W, U) → κ
  59. Angle(W, U, V) → λ
  60. Angle(U, V, T) → μ
  61. Segment(T, U) → f_2
  62. Segment(V, W) → g_2
  63. Distance(T, U) → distanceTU
  64. Distance(W, V) → distanceWV
  65. Distance(V, U) → distanceVU
  66. Distance(U, W) → distanceUW
  67. Intersect(f_2, g_2) → Z
  68. Distance(T, Z) → distanceTZ
  69. Distance(Z, U) → distanceZU
  70. Distance(V, Z) → distanceVZ
  71. Distance(Z, W) → distanceZW
  72. Intersect(d_2, e_2) → A_1
  73. Distance(E, A_1) → distanceEA1
  74. Distance(A_1, G) → distanceA1G
  75. Distance(A_1, I) → distanceA1I
  76. Distance(A_1, F) → distanceA1F
  77. Intersect(b_2, c_2) → B_1
  78. Distance(A, B_1) → distanceAB1
  79. Distance(B_1, C) → distanceB1C
  80. Distance(B_1, B) → distanceB1B
  81. Distance(B_1, D) → distanceB1D
  82. Angle(M, L, N) → ν
  83. Angle(L, N, O) → ξ
  84. Angle(N, O, M) → ο
  85. Angle(O, M, L) → ρ
  86. Segment(L, O) → h_2
  87. Segment(N, M) → i_2
  88. Intersect(h_2, i_2) → C_1
  89. Distance(L, C_1) → distanceLC1
  90. Distance(C_1, O) → distanceC1O
  91. Distance(C_1, M) → distanceC1M
  92. Distance(C_1, N) → distanceC1N
  93. Distance(M, O) → distanceMO
  94. Distance(O, N) → distanceON
  95. Distance(E, G) → distanceEG
  96. Distance(G, I) → distanceGI

AI 绘图提示语参考

绘制一个平行四边形,使用点A和B作为对角线的两个端点,通过旋转和构造平行线来创建其他边。首先,构造一个四边形ABCD,然后通过旋转点D和点C来创建新的点D'和C',并连接这些点形成新的平行四边形。接着,通过点A和B构造对角线,使用线段和旋转命令创建平行四边形的其他边,最后通过旋转和构造平行线来完成整个图形的构建。
以上提示语为根据原始绘图命令整理而来,仅供参考。