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三角形内角和定理演示 by John Williams

三角形内角和定理演示 by John Williams
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2016-11-07 08:08
测试改名0角变换几何作图
①本范例通过动态演示，直观展示三角形内角和为180°的几何定理；②涉及核心概念包括三角形、角度测量、几何变换；③构造过程中运用了Segment（线段）、Polygon（多边形）、Angle（角度）、Rotate（旋转）、Vector（向量）等GeoGebra命令与对象；④适合初中及以上学生用于理解几何定理和变换思想，也可用于数学教学演示。

GeoGebra 命令及参数

  1. Segment(B, C) → e
  2. Segment(C, A) → f
  3. Min(f, e) → m
  4. Segment(A, B) → d
  5. Min(d, f) → o
  6. Min(m, o) → u
  7. Polygon(A, B, C) → poly1, c, a, b
  8. Ray(A, B) → h
  9. Ray(B, C) → i
  10. Ray(C, A) → j
  11. Circle(C, (0.25 * u)) → p
  12. Circle(A, (0.25 * u)) → q
  13. Circle(B, (0.25 * u)) → r
  14. Intersect(p, f) → D,
  15. Intersect(p, e, 1) → E
  16. Intersect(r, e, 1) → F
  17. Intersect(r, d, 1) → G
  18. Intersect(q, d, 1) → H
  19. Intersect(q, f, 1) → I
  20. Intersect(r, h, 2) → J
  21. Intersect(q, j, 2) → K
  22. Intersect(p, i, 2) → L
  23. Midpoint(f) → M
  24. Midpoint(e) → N
  25. CircleSector(A, H, I) → s
  26. CircleSector(B, F, G) → t
  27. CircleSector(C, D, E) → c_1
  28. Angle(A, C, B) → α
  29. CircleSector(C, E, D) → d_1
  30. CircleSector(A, I, H) → e_1
  31. CircleSector(B, G, F) → f_1
  32. Min(d, e) → n
  33. Rotate(s, If[0 < l ≤ 1, (((-l) * 180))°, -180°], M) → s'
  34. Rotate(A, If[0 < l ≤ 1, (((-l) * 180))°, -180°], M) → A'
  35. Segment(M, A') → a_1
  36. Rotate(H, -180°, M) → H'
  37. Line(H', C) → b_1
  38. Rotate(B, If[0 < l ≤ 1, ((l * 180))°, 180°], N) → B'
  39. Rotate(t, If[0 < l ≤ 1, ((l * 180))°, 180°], N) → t'
  40. Segment(N, B') → g_1
  41. Segment(C, M) → h_1
  42. Segment(M, A) → i_1
  43. Segment(C, N) → j_1
  44. Segment(N, B) → k_1
  45. Rotate(A, If[0 < l ≤ 1, ((l * 180))°, -180°], M) → A'_1
  46. Rotate(B, If[0 < l ≤ 1, (((-l) * 180))°, -180°], N) → B'_1
  47. Segment(N, B'_1) → l_1
  48. Segment(M, A'_1) → m_1
  49. Rotate(e_1, If[0 < l ≤ 1, ((l * 180))°, -180°], M) → p_1
  50. Rotate(f_1, If[0 < l ≤ 1, (((-l) * 180))°, -180°], N) → q_1
  51. CircleSector(C, L, D) → r_1
  52. CircleSector(A, K, H) → s_1
  53. CircleSector(B, J, F) → t_1
  54. CircleSector(A, H, K) → c_2
  55. CircleSector(B, F, J) → d_2
  56. CircleSector(C, D, L) → e_2
  57. Dilate(A, 1 - v, C) → A'_2
  58. Dilate(B, 1 - v, C) → B'_2
  59. Vector(A, A'_2) → w
  60. Vector(B, B'_2) → u_1
  61. Translate(s_1, w) → f_2
  62. CircleArc(A, K, H) → g_2
  63. Translate(t_1, u_1) → h_2
  64. CircleArc(B, J, F) → k_2
  65. Translate(c_2, w) → p_2
  66. CircleArc(A, H, K) → q_2
  67. Translate(d_2, u_1) → r_2
  68. CircleArc(B, F, J) → s_2