相似矩形的动态演示

相似矩形的动态演示
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2017-04-09 05:58
这是一个动态可修改的三角形两边上构建相似矩形的定理演示。通过旋转、射线、点、线段等 GeoGebra 命令,可以直观地展示相似矩形的性质。适合初中及以上学生学习相似形和三角形相关知识。

GeoGebra 命令及参数

  1. Rotate(A, (a_4 * π / 180), B) → A'
  2. Ray(B, A') → g
  3. Point(g) → C
  4. Segment(B, C) → a
  5. OrthogonalLine(C, a) → s
  6. Segment(C, A) → b
  7. OrthogonalLine(A, b) → l
  8. Point(l) → D
  9. Ray(A, D) → m
  10. Point(m) → E
  11. Line(B, E) → p_1
  12. Segment(A, E) → r
  13. Circle(C, (b_3 * a)) → c
  14. Intersect(c, s) → G, H
  15. Line(H, a) → t
  16. OrthogonalLine(B, t) → d
  17. Intersect(t, d) → I
  18. Line(I, A) → q_1
  19. Angle(A, B, A') → α
  20. Ray(B, A) → f
  21. Line(B, A) → i
  22. OrthogonalLine(C, b) → k
  23. OrthogonalLine(E, m) → n
  24. Intersect(k, n) → F
  25. Segment(C, F) → p
  26. Segment(F, E) → q
  27. Segment(H, C) → e
  28. Segment(B, I) → f_1
  29. Segment(I, H) → g_1
  30. OrthogonalLine(C, i) → h_1
  31. Intersect(i, h_1) → J
  32. Angle(C, J, B) → β
  33. Segment(B, E) → i_1
  34. Segment(A, I) → j_1
  35. Dilate(B, If[0 < u ≤ 1, 1 - u, 0], E) → B'
  36. Segment(B, B') → k_1
  37. Dilate(A, If[1 < u ≤ 2, 2 - u, 0], I) → A'_1
  38. Segment(A, A'_1) → l_1
  39. Intersect(p_1, q_1) → K
  40. Dilate(C, If[2 < u ≤ 3, 3 - u, 0], K) → C'
  41. Segment(C, C') → m_1
  42. Dilate(K, If[3 < u ≤ 4, 4 - u, 0], J) → K'
  43. Segment(K, K') → n_1
  44. Line(C, J) → r_1
  45. Circle(C, 1) → c_1
  46. Intersect(c_1, r_1, 1) → L
  47. Ray(C, L) → s_1
  48. Line(J, C) → t_1
  49. Circle(J, 1) → d_1
  50. Intersect(d_1, t_1, 1) → M
  51. Ray(J, M) → a_1
  52. Polygon(B, A, C) → poly1, c_2, b_1, a_2
  53. Polygon(A, E, F, C) → poly2, a_3, e_1, f_2, c_3
  54. Polygon(C, H, I, B) → poly3, c_4, h_2, i_2, b_2
  55. Angle(C, B, I) → γ
  56. Angle(H, C, B) → δ
  57. Angle(I, H, C) → ε
  58. Angle(A, C, F) → ζ
  59. Angle(C, F, E) → η
  60. Angle(E, A, C) → θ
  61. Min(a, Distance[A, B]) → v
  62. Circle(B, (0.2 * a)) → d_2
  63. Intersect(d_2, i, 2) → N
  64. Intersect(d_2, a, 1) → O
  65. CircleSector(B, N, O) → e_2