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边边边判定定理的动态证明

边边边判定定理的动态证明
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2017-11-30 02:57
测试改名0变换几何作图滑块动画
①本范例演示了三角形边边边判定定理的动态证明过程；②涉及的核心数学概念包括三角形全等判定、几何变换（反射、旋转、平移）；③作图要点——使用了GeoGebra命令：Circle（圆）、Intersect（交点）、Segment（线段）、Polygon（多边形）、Point（点）、Line（直线）、Angle（角）、Dilate（缩放）、Vector（向量）、Translate（平移）、Rotate（旋转）、Mirror（反射）、Ray（射线）；④适合高中数学学生及教师用于理解和教学三角形全等判定定理。

GeoGebra 命令及参数

  1. Circle(A, a) → d
  2. Intersect(d, e) → B, C
  3. Circle(C, b) → f
  4. Segment(A, C) → g
  5. Circle(A, c) → k
  6. Intersect(k, f) → F, G, ,
  7. Segment(C, F) → h
  8. Segment(F, A) → i
  9. Polygon(A, C, F) → poly1, f_1, a_1, c_1
  10. Circle(D, i) → p
  11. Point(p) → E
  12. Segment(D, E) → n
  13. Circle(D, g) → q
  14. Circle(E, h) → r
  15. Intersect(q, r, 2) → H
  16. Segment(D, H) → s
  17. Segment(H, E) → t
  18. Line(A, n) → g_1
  19. Point(g_1) → I
  20. Angle(I, A, F) → α
  21. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], D) → A'
  22. Vector(A, A') → u
  23. Translate(F, u) → F'
  24. Translate(A, u) → A'_1
  25. Segment(F', A'_1) → i'
  26. Rotate(F', If[1 < o ≤ 2, ((-(o - 1)) * α), (-α)], D) → F''
  27. Rotate(A'_1, If[1 < o ≤ 2, ((-(o - 1)) * α), (-α)], D) → J
  28. Segment(F'', J) → i''
  29. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], D) → A'_2
  30. Vector(A, A'_2) → v
  31. Translate(A, v) → A'_3
  32. Translate(C, v) → C'
  33. Segment(A'_3, C') → g'
  34. Line(D, g) → h_1
  35. Point(h_1) → K
  36. Angle(H, D, K) → β
  37. Rotate(A'_3, If[3 < o ≤ 4, ((-(o - 3)) * β), (-β)], D) → L
  38. Rotate(C', If[3 < o ≤ 4, ((-(o - 3)) * β), (-β)], D) → C''
  39. Segment(L, C'') → g''
  40. Line(C, t) → i_1
  41. Point(i_1) → M
  42. Angle(M, C, F) → γ
  43. Dilate(C, If[4 < o ≤ 5, 5 - o, 0], C'') → C'_1
  44. Vector(C, C'_1) → w
  45. Translate(C, w) → C'_2
  46. Translate(F, w) → F'_1
  47. Segment(C'_2, F'_1) → h'
  48. Rotate(C'_2, If[5 < o ≤ 6, ((-(o - 5)) * γ), (-γ)], C'') → N
  49. Rotate(F'_1, If[5 < o ≤ 6, ((-(o - 5)) * γ), (-γ)], C'') → O
  50. Segment(N, O) → h''
  51. Polygon(D, C'', E) → poly2, e_1, d_1, c''
  52. Dilate(A, If[(6 * 0.5) < o ≤ 7.5, 7.5 - o, 0], D) → A'_4
  53. Vector(A, A'_4) → u_1
  54. Translate(A, u_1) → A'_5
  55. Translate(C, u_1) → C'_3
  56. Translate(F, u_1) → F'_2
  57. Polygon(A'_5, C'_3, F'_2) → poly1', f'_2, a'_5, c'_3
  58. Rotate(A'_5, If[7.5 < o ≤ 8.5, ((-(o - 7.5)) * γ), (-γ)], D) → P
  59. Rotate(C'_3, If[7.5 < o ≤ 8.5, ((-(o - 7.5)) * γ), (-γ)], D) → Q
  60. Rotate(F'_2, If[7.5 < o ≤ 8.5, ((-(o - 7.5)) * γ), (-γ)], D) → R
  61. Polygon(P, Q, R) → poly1'', r_1, p_1, q_1
  62. Line(F, C) → j_1
  63. Mirror(A, j_1) → A'_6
  64. Mirror(C, j_1) → C'_4
  65. Mirror(F, j_1) → F'_3
  66. Polygon(A'_6, C'_4, F'_3) → poly1'_1, f'_3, a'_6, c'_4
  67. Point(j_1) → S
  68. Point(j_1) → T
  69. Ray(C'_4, T) → k_1
  70. Ray(F'_3, S) → l_1
  71. Segment(A'_6, F'_3) → m_1
  72. Segment(A'_6, C'_4) → n_1