平行四边形、矩形与正方形的几何性质与作图演示

平行四边形、矩形与正方形的几何性质与作图演示
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2012-09-26 19:11
本 GeoGebra 范例动态演示了平行四边形、矩形、菱形和正方形等特殊四边形的几何构造及其核心性质。核心数学概念包括平行四边形的边角关系、面积与周长计算、对角线性质(如垂直与平分)以及相关的圆。作图要点上,该课件通过 GeoGebra 的 Point、Segment、Rotate、Angle、Line、Intersect、OrthogonalLine、Polygon 和 Circle 等几何作图命令,结合参数 a, b, α 和顶点 A, B, C, D 等对象,生动展现了从一般平行四边形向矩形、正方形过渡时几何特征的变化。本工具非常适合中学及大学阶段的几何学习、课堂演示或自主探究。

GeoGebra 命令及参数

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → AB
  3. Point(Circle[A, b]) → Dpomocna
  4. Segment(A, Dpomocna) → b'pomocni
  5. Rotate(Dpomocna, α, A) → D
  6. Angle(Dpomocna, A, D) → α_1
  7. Segment(A, D) → AD_1
  8. Line(D, AB) → la
  9. Line(B, AD_1) → lb
  10. Intersect(la, lb) → C
  11. Line(A, B) → lAB
  12. OrthogonalLine(D, lAB) → n_a
  13. Intersect(n_a, lAB) → E
  14. Segment(D, E) → h_a
  15. Polygon(A, B, C, D) → Paralelogram, a_0, b_0, c_0, d_0
  16. Polygon(A_2, B_2, C_2, D_2) → Pravougaonik, a_2, b_2, c_2, d_2
  17. Angle(B_2, A_2, D_2) → αP
  18. Polygon(A_3, B_3, C_3, D_3) → Kvadrat, a_3, b_3, c_3, d_3
  19. Polygon(A_4, B_4, C_4, D_4) → Romb, a_4, b_4, c_4, d_4
  20. Angle(B_3, A_3, D_3) → αK
  21. Angle(B_4, A_4, D_4) → αR
  22. Segment(D_4, Er_1) → h
  23. Segment(A, C) → AC
  24. Segment(B, D) → BD
  25. Intersect(AC, BD) → O
  26. Segment(B_2, D_2) → dp
  27. Segment(A_2, C_2) → dp_1
  28. Intersect(dp, dp_1) → O_1
  29. Segment(D_3, B_3) → dk
  30. Segment(A_3, C_3) → dk_1
  31. Segment(A_4, C_4) → dr1
  32. Segment(B_4, D_4) → dr2
  33. Intersect(dr2, dr1) → O_3
  34. Intersect(dk_1, dk) → O_2
  35. Circle(O_1, A_2) → k_p
  36. Circle(O_3, h / 2) → k_r
  37. Segment(O_1, B_2) → r_p
  38. Intersect(k_r, a_4) → Er_2,
  39. Segment(O_3, Er_2) → r_r
  40. Circle(O_2, dk / 2) → k_o
  41. Circle(O_2, a / 2) → k_u
  42. Segment(O_2, B_3) → r_o
  43. Intersect(k_u, a_3) → Ek,
  44. Segment(O_2, Ek) → r_u
  45. OrthogonalLine(D, lb) → n_b
  46. Intersect(lb, n_b) → F
  47. Segment(D, F) → h_b
  48. Point(lAB) → A_1
  49. Point(la) → D_1
  50. Polygon(A_1, B_1, C_1, D_1) → P, a_1, b_1, c_1, d_1
  51. Segment(D_1, E_0) → ha_0
  52. Angle(D, C, B) → γ
  53. Angle(C, B, A) → β
  54. Angle(A, D, C) → δ
  55. Angle(B_4, O_3, C_4) → αRd
  56. Segment(O_3, C_4) → dr1p
  57. Segment(B_4, O_3) → dr2p
  58. Angle(B_4, A_4, O_3) → αR_1
  59. Angle(O_3, A_4, D_4) → αR_2