特殊平行四边形探索

特殊平行四边形探索
几何画板及绘图内容加载中,请稍等……
2018-01-11 08:21
①本范例演示特殊平行四边形(如矩形、菱形、正方形)的几何性质与相互关系;②涉及核心概念包括平行四边形定义、对角线性质、角与边的关系、几何作图等;③通过 GeoGebra 命令如 Segment(线段)、OrthogonalLine(垂线)、Point(点)、Line(直线)、Intersect(交点)、Polygon(多边形)、Distance(距离)、Angle(角度)、LineBisector(角平分线)、Circle(圆)等实现;④适合高中数学教学,用于直观理解平行四边形分类与性质,及优化问题中的几何应用。

GeoGebra 命令及参数

  1. Segment(F, G) → f
  2. OrthogonalLine(F, f) → g
  3. OrthogonalLine(G, f) → h
  4. Point(g) → H
  5. Line(H, f) → i
  6. Intersect(h, i) → I
  7. Polygon(H, I, G, F) → poly2, h_1, i_1, g_1, f_1
  8. Segment(J, K) → j
  9. Polygon(J, K, 4) → poly3, k, l, m, n, L, M
  10. Segment(N, O) → p
  11. Line(P, p) → q
  12. Segment(O, P) → r
  13. Line(N, r) → s
  14. Intersect(q, s) → Q
  15. Polygon(P, Q, N, O) → poly4, p_1, q_1, n_1, o
  16. Distance(P, O) → distancePO
  17. Distance(O, N) → distanceON
  18. Distance(N, Q) → distanceNQ
  19. Distance(Q, P) → distanceQP
  20. Distance(F, G) → distanceFG
  21. Distance(F, H) → distanceFH
  22. Distance(H, I) → distanceHI
  23. Distance(I, G) → distanceIG
  24. Distance(K, J) → distanceKJ
  25. Distance(J, M) → distanceJM
  26. Distance(M, L) → distanceML
  27. Distance(L, K) → distanceLK
  28. Angle(poly4) → α, β, γ, δ
  29. Angle(poly2) → ε, ζ, η, θ
  30. Angle(poly3) → ν, ξ, ο, ρ
  31. Segment(O, Q) → b_1
  32. Segment(P, N) → c_1
  33. Segment(H, G) → e_1
  34. Segment(I, F) → j_1
  35. Segment(K, M) → m_1
  36. Segment(L, J) → r_1
  37. Intersect(b_1, c_1) → R
  38. Intersect(e_1, j_1) → S
  39. Intersect(m_1, r_1) → U
  40. Angle(K, U, L) → σ
  41. Distance(O, R) → distanceOR
  42. Distance(R, Q) → distanceRQ
  43. Distance(P, R) → distancePR
  44. Distance(R, N) → distanceRN
  45. Distance(F, S) → distanceFS
  46. Distance(S, I) → distanceSI
  47. Distance(H, S) → distanceHS
  48. Distance(S, G) → distanceSG
  49. Distance(K, U) → distanceKU
  50. Distance(U, J) → distanceUJ
  51. Distance(U, M) → distanceUM
  52. Distance(U, L) → distanceUL
  53. Segment(A, B) → a
  54. LineBisector(a) → b
  55. Point(b) → C
  56. Intersect(b, a) → D
  57. Circle(D, Segment[D, C]) → c
  58. Intersect(c, b, 2) → E
  59. Polygon(C, B, E, A) → poly1, c_2, b_2, e, a_1
  60. Segment(C, E) → d
  61. Segment(B, A) → d_1
  62. Angle(C, D, B) → ι
  63. Distance(D, A) → distanceDA
  64. Distance(B, D) → distanceBD
  65. Distance(D, E) → distanceDE
  66. Distance(C, D) → distanceCD
  67. Angle(poly1) → κ, λ, μ, τ
  68. Segment(B, E) → k_1
  69. Segment(E, A) → l_1
  70. Segment(A, C) → s_1
  71. Segment(C, B) → t_1

AI 绘图提示语参考

画一个平行四边形,并分别画出两条对角线,交点为I。以F、G为顶点画出平行四边形FGHI,再以J、K为顶点画出四边形JKML,最后以N、O为顶点画出平行四边形NOPQ。测量所有边长和角度,并标注出关键点的距离和角度关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。