三角形全等判定:SSS与SAS的几何作图

三角形全等判定:SSS与SAS的几何作图
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2022-07-16 22:21
本范例演示如何使用GeoGebra工具绘制三角形,并验证SSS(边边边)和SAS(边角边)全等判定条件。核心数学概念包括三角形全等、几何作图与距离计算。作图要点涉及使用Line、Point、Segment、Circle等命令构造三角形,并通过Distance和Midpoint命令验证边长与角度。适合初中生学习几何全等概念,或用于数学教学演示。

GeoGebra 命令及参数

  1. Line(A, B) → a
  2. Point(a) → F
  3. Point(a) → E
  4. Segment(E, F) → d
  5. Point(a) → D
  6. Point(a) → C
  7. Segment(C, D) → b
  8. Circle(K, b) → g
  9. Point(g) → I
  10. Angle(Line[K, I], y = 0) → angle1
  11. Point(a) → L
  12. Point(a) → G
  13. Segment(G, L) → e
  14. Point(a) → H
  15. Circle(K, b) → c
  16. Circle(N, b) → f
  17. Circle(N, b) → k
  18. Segment(K, I) → j
  19. Point(k) → M
  20. Segment(N, M) → m
  21. Circle(K, e) → p
  22. Circle(N, e) → q
  23. Point(p) → O
  24. Segment(K, O) → n
  25. Point(q) → P
  26. Segment(N, P) → r
  27. Circle(I, d) → h
  28. Circle(M, d) → s
  29. Point(h) → J
  30. Segment(I, J) → i
  31. Point(s) → Q
  32. Segment(M, Q) → t
  33. Angle(O, K, I) → α
  34. Angle(J, I, K) → β
  35. Angle(P, N, M) → γ
  36. Angle(Q, M, N) → δ
  37. Circle(O, 0.05) → c_1
  38. Circle(P, 0.05) → d_1
  39. If(IsInRegion[Q, d_1], Angle[N, P, M]) → ε
  40. If(IsInRegion[J, c_1], Angle[K, O, I]) → ζ
  41. Angle(Line[N, M], y = 0) → angle3
  42. Distance(O, J) → o
  43. Distance(O, R) → v
  44. Distance(O, S) → w
  45. Distance(P, Q) → a_{1}
  46. Distance(P, T) → b_{1}
  47. Distance(P, U) → e_{1}
  48. Midpoint(O, K) → G_1
  49. Midpoint(K, I) → H_1
  50. Midpoint(I, J) → I_1
  51. Midpoint(N, P) → J_1
  52. Midpoint(N, M) → K_1
  53. Midpoint(M, Q) → L_1
  54. Midpoint(G, L) → M_1
  55. Midpoint(C, D) → N_1
  56. Midpoint(E, F) → O_1
  57. Circle(K, 1) → f_1
  58. AngularBisector(O, K, I) → g_1
  59. Intersect(f_1, g_1, 2) → P_1
  60. Circle(I, 1) → h_1
  61. AngularBisector(K, I, J) → i_1
  62. Intersect(h_1, i_1, 2) → Q_1
  63. Circle(J, 1) → p_1
  64. AngularBisector(K, O, I) → l_1
  65. Intersect(p_1, l_1, 2) → R_1
  66. Angle(O, K, I) → η
  67. If(IsInRegion[J, c_1], Angle[K, O, I]) → θ
  68. Angle(J, I, K) → ι
  69. Circle(N, 1) → q_1
  70. Circle(Q, 1) → r_1
  71. Circle(M, 1) → s_1
  72. AngularBisector(P, N, M) → m_1
  73. AngularBisector(N, M, Q) → n_1
  74. AngularBisector(N, P, M) → t_1
  75. Intersect(q_1, m_1, 2) → S_1
  76. Intersect(s_1, n_1, 2) → T_1
  77. Intersect(r_1, t_1, 2) → U_1
  78. If(IsInRegion[Q, d_1], Angle[N, P, M]) → κ
  79. Angle(P, N, M) → λ
  80. Angle(Q, M, N) → μ

AI 绘图提示语参考

绘制两个三角形,三角形ABC和DEF,使用SSS和SAS准则验证它们的全等性。首先画线段AB,然后在该线上依次放置点E、F、D、C,接着画线段CD和EF,确保它们的长度相等。使用圆和角度工具,构造三角形DEF,使其与三角形ABC的边长和角度相匹配。最后,验证三角形DEF的边长和角度是否与三角形ABC相等。
以上提示语为根据原始绘图命令整理而来,仅供参考。