平行四边形、正方形、矩形、菱形

平行四边形、正方形、矩形、菱形
几何画板及绘图内容加载中,请稍等……
2018-02-09 01:51
这个范例演示了平行四边形、正方形、矩形和菱形的几何构造。涉及的核心数学概念包括平行线、垂直线、距离、角度等。通过使用GeoGebra命令如Segment、Line、Intersect、Polygon等,可以直观地展示这些图形的性质。适合初中及以上学生学习几何作图。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Segment(A, C) → g
  3. Line(C, f) → h
  4. Line(B, g) → i
  5. Intersect(h, i) → D
  6. Polygon(C, A, B, D) → q1, c, a, b, d
  7. Distance(g, d) → e
  8. Angle(C, D, B) → α
  9. Angle(C, A, B) → β
  10. Angle(D, C, A) → γ
  11. Angle(D, B, A) → δ
  12. Segment(B, C) → j
  13. Segment(A, D) → k
  14. Intersect(j, k) → E
  15. Distance(B, E) → distanceBE
  16. Distance(A, E) → distanceAE
  17. Distance(D, E) → distanceDE
  18. Distance(C, E) → distanceCE
  19. Segment(F, G) → l
  20. Circle(F, G) → p
  21. Point(p) → H
  22. Segment(F, H) → m
  23. Line(H, l) → n
  24. Line(G, m) → q
  25. Intersect(n, q) → I
  26. Segment(H, I) → r
  27. Segment(G, I) → s
  28. Polygon(I, G, F, H) → q2, i_1, g_1, f_1, h_1
  29. Angle(G, F, H) → ε
  30. Angle(H, I, G) → ζ
  31. Angle(F, H, I) → η
  32. Angle(F, G, I) → θ
  33. Segment(J, K) → t
  34. OrthogonalLine(J, t) → j_1
  35. OrthogonalLine(K, t) → k_1
  36. Circle(J, K) → c_1
  37. Intersect(c_1, j_1, 2) → L
  38. OrthogonalLine(L, j_1) → l_1
  39. Intersect(k_1, l_1) → M
  40. Segment(J, L) → m_1
  41. Segment(L, M) → n_1
  42. Segment(K, M) → p_1
  43. Polygon(J, L, M, K) → q3, j_2, l_2, m_2, k_2
  44. Distance(H, I) → distanceHI
  45. Distance(G, I) → distanceGI
  46. Distance(F, G) → distanceFG
  47. Distance(H, F) → distanceHF
  48. Angle(J, L, M) → ι
  49. Angle(J, K, M) → κ
  50. Angle(L, J, K) → λ
  51. Angle(K, M, L) → μ
  52. Distance(m_1, p_1) → o
  53. Distance(J, K) → distanceJK
  54. Distance(K, M) → distanceKM
  55. Distance(M, L) → distanceML
  56. Distance(L, J) → distanceLJ
  57. Segment(N, O) → q_1
  58. OrthogonalLine(N, q_1) → r_1
  59. OrthogonalLine(O, q_1) → s_1
  60. Point(s_1) → P
  61. Line(P, q_1) → t_1
  62. Intersect(r_1, t_1) → Q
  63. Segment(N, Q) → a_1
  64. Segment(Q, P) → b_1
  65. Segment(P, O) → d_1
  66. Angle(N, Q, P) → ν
  67. Angle(Q, N, O) → ξ
  68. Angle(O, P, Q) → ο
  69. Angle(N, O, P) → ρ
  70. Distance(Q, N) → distanceQN
  71. Midpoint(Q, N) →
  72. Distance(O, P) → distanceOP
  73. Midpoint(O, P) →
  74. Distance(N, O) → distanceNO
  75. Midpoint(N, O) →
  76. Distance(Q, P) → distanceQP
  77. Midpoint(Q, P) →
  78. Polygon(N, Q, P, O) → q4, n_2, q_2, p_2, o_1

AI 绘图提示语参考

绘制一个平行四边形,然后依次构造一个正方形、一个矩形和一个菱形。首先,画出两条平行线段AB和AC,接着画一条与AC平行的直线BC,再画一条与AB平行的直线BD,交点为D。然后,连接点A、B、C、D形成平行四边形。接着,测量边长和角度,确保AB=CD,AD=BC,且角ABC=角CDA。进一步构造正方形,确保AB=BC=CD=DA,所有角都是直角。再构造矩形,确保AB=CD,AD=BC,且角ABC=角CDA=角ADC=角DAB。最后,构造菱形,确保AB=BC=CD=DA,且角ABC+角BCD=180度。
以上提示语为根据原始绘图命令整理而来,仅供参考。