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全等定理的动态演示与几何构造

全等定理的动态演示与几何构造
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2018-04-29 15:44
测试改名0多边形角变换几何作图
该范例通过GeoGebra交互式几何环境，动态演示了三角形全等判定定理（如SSS、SAS、ASA等）的图形构造与验证过程。核心数学概念包括全等三角形的对应边、对应角相等关系，以及多边形、周长、中位线等基础几何性质。作图要点：利用Polygon命令创建初始三角形poly1，通过Circle、Point、Segment、Intersect等命令构造辅助圆与交点，结合Angle、Rotate、Ray命令实现旋转与角度测量，并生成多个关联对象（如D、F、G、E_1等）以展示不同全等情形；最终通过文本对象text1标注结论。适合中学几何教学，用于直观理解全等判定条件，也可作为教师制作动态课件的参考模板。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Circle(A, B) → d
  3. Circle(C, B) → e
  4. Circle(D, c) → f
  5. Point(Circle[D, abs(b)]) → F
  6. Segment(D, F) → g
  7. Circle(F, a) → h
  8. Intersect(h, f) → E_1, G, ,
  9. Polygon(D, F, G) → poly2, g_1, d_1, f_1
  10. Segment(A, C) → i
  11. Segment(D, F) → j
  12. Segment(A, B) → k
  13. Segment(D, G) → l
  14. Segment(C, B) → m
  15. Segment(F, G) → n
  16. Segment(H, I) → p
  17. Segment(H, J) → q
  18. Angle(I, H, J) → α
  19. Segment(J, I) → r
  20. Point(Circle[K, abs(q)]) → L
  21. Segment(K, L) → s
  22. Rotate(K, (-α), L) → K'
  23. Angle(K', L, K) → β
  24. Ray(L, K') → t
  25. Circle(L, p) → c_1
  26. Intersect(c_1, t) → M,
  27. Segment(M, K) → a_1
  28. Segment(L, M) → b_1
  29. Segment(N, O) → e_1
  30. Segment(P, N) → h_1
  31. Segment(P, O) → i_1
  32. Angle(O, N, P) → γ
  33. Angle(P, O, N) → δ
  34. Point(Circle[Q, abs(e_1)]) → R
  35. Segment(Q, R) → j_1
  36. Rotate(R, γ, Q) → R'
  37. Angle(R, Q, R') → ε
  38. Rotate(Q, (-δ), R) → Q'
  39. Angle(Q', R, Q) → ζ
  40. Ray(Q, R') → k_1
  41. Ray(R, Q') → l_1
  42. Intersect(k_1, l_1) → S
  43. Segment(S, Q) → m_1
  44. Segment(S, R) → n_1
  45. Segment(T, U) → p_1
  46. Segment(U, V) → q_1
  47. Segment(V, T) → r_1
  48. Point(Circle[W, abs(p_1)]) → Z
  49. Segment(W, Z) → t_1
  50. Angle(T, U, V) → η
  51. Angle(U, V, T) → θ
  52. Rotate(W, η, Z) → W'
  53. Angle(W, Z, W') → ι
  54. Angle(V, T, U) → κ
  55. Rotate(Z, (-κ), W) → Z'
  56. Angle(Z', W, Z) → λ
  57. Ray(Z, W') → a_2
  58. Ray(W, Z') → b_2
  59. Intersect(b_2, a_2) → E
  60. Segment(W, E) → c_2
  61. Segment(E, Z) → d_2
  62. Angle(Z, E, W) → μ
  63. Segment(A, B) → e_2
  64. Segment(A, C) → f_2
  65. Segment(C, B) → h_2
  66. Segment(G, D) → i_2
  67. Segment(D, F) → j_2
  68. Segment(G, F) → k_2
  69. Segment(K, L) → l_2
  70. Segment(L, M) → m_2
  71. Segment(J, H) → n_2
  72. Segment(H, I) → p_2
  73. Angle(M, L, K) → ν
  74. Angle(I, H, J) → ξ
  75. Segment(N, O) → q_2
  76. Segment(Q, R) → r_2
  77. Angle(O, N, P) → ο
  78. Angle(R, Q, S) → ρ
  79. Angle(P, O, N) → σ
  80. Angle(S, R, Q) → τ
  81. Segment(U, T) → s_2
  82. Segment(Z, W) → t_2
  83. Angle(T, U, V) → υ
  84. Angle(W, Z, E) → ϕ
  85. Angle(U, V, T) → χ
  86. Angle(Z, E, W) → ψ