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SSS全等三角形判定与作图

SSS全等三角形判定与作图
几何画板及绘图内容加载中，请稍等……
2019-04-21 08:23
测试改名0向量几何作图
本范例演示如何利用SSS（边边边）判定全等三角形，并通过GeoGebra进行动态作图。核心数学概念包括三角形全等判定、几何作图与变换。作图要点涉及使用Circle、Intersect、Segment等GeoGebra命令构建三角形及验证全等关系。适合初中生学习几何全等概念，或用于几何教学演示。

GeoGebra 命令及参数

  1. Circle(A, a) → d_1
  2. Intersect(d_1, 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. Line(F, C) → j_1
  52. Mirror(A, j_1) → A'_6
  53. Mirror(C, j_1) → C'_4
  54. Mirror(F, j_1) → F'_3
  55. Polygon(A'_6, C'_4, F'_3) → poly1'_1, f'_3, a'_6, c'_4
  56. Point(j_1) → S
  57. Point(j_1) → T
  58. Ray(C'_4, T) → k_1
  59. Ray(F'_3, S) → l_1
  60. Segment(A'_6, F'_3) → m_1
  61. Segment(A'_6, C'_4) → n_1
  62. Dilate(F, If[0 < d ≤ 1, 1 - d, 0], E) → F'_2
  63. Vector(F, F'_2) → u_1
  64. Translate(A'_6, u_1) → P
  65. Translate(C'_4, u_1) → Q
  66. Translate(F'_3, u_1) → R
  67. Polygon(P, Q, R) → poly2, r_1, p_1, q_1
  68. Translate(A'_6, u_1) → U
  69. Translate(C'_4, u_1) → V
  70. Segment(U, V) → s_1
  71. Translate(A'_6, u_1) → W
  72. Translate(F'_3, u_1) → Z
  73. Segment(W, Z) → t_1
  74. Translate(C, u_1) → C'_3
  75. Translate(F, u_1) → F'_4
  76. Segment(C'_3, F'_4) → h'_1
  77. Translate(A'_6, u_1) → A_1
  78. Translate(F'_3, u_1) → B_1
  79. Segment(A_1, B_1) → e_1
  80. Line(E, k_1) → f_2
  81. Point(f_2) → C_1
  82. Angle(C'', E, C_1) → δ
  83. Rotate(P, If[1 < d ≤ 2, ((-(d - 1)) * δ), (-δ)], E) → P'
  84. Rotate(Q, If[1 < d ≤ 2, ((-(d - 1)) * δ), (-δ)], E) → Q'
  85. Rotate(R, If[1 < d ≤ 2, ((-(d - 1)) * δ), (-δ)], E) → R'
  86. Polygon(P', Q', R') → poly2', r', p', q'
  87. Rotate(A_1, If[1 < d ≤ 2, ((-(d - 1)) * δ), (-δ)], E) → D_1
  88. Rotate(B_1, If[1 < d ≤ 2, ((-(d - 1)) * δ), (-δ)], E) → E_1
  89. Segment(D_1, E_1) → g_2
  90. Rotate(U, If[1 < d ≤ 2, ((-(d - 1)) * δ), (-δ)], E) → U'
  91. Rotate(V, If[1 < d ≤ 2, ((-(d - 1)) * δ), (-δ)], E) → V'
  92. Segment(U', V') → h_2
  93. Rotate(C'_3, If[1 < d ≤ 2, ((-(d - 1)) * δ), (-δ)], E) → F_1
  94. Rotate(F'_4, If[1 < d ≤ 2, ((-(d - 1)) * δ), (-δ)], E) → G_1
  95. Segment(F_1, G_1) → i_2
  96. Polygon(D, C'', E) → poly3, e_2, d_2, c''
  97. Dilate(D, If[2.5 < d ≤ 3.5, 3.5 - d, 0], D_1) → D'
  98. Segment(D, D') → j_2
  99. Segment(E, C'') → k_2
  100. Min(c, k_2 / 2) → o_1
  101. Circle(D, (0.3 * o_1)) → c_2
  102. Intersect(c_2, i'') → H_1,
  103. Intersect(c_2, j_2) → I_1,
  104. CircleSector(D, I_1, H_1) → p_2
  105. Intersect(j_2, k_2) → J_1
  106. Polygon(D, D_1, E) → poly4, e_3, d_3, d_4
  107. Dilate(D, If[3.5 < d ≤ 4.5, 4.5 - d, 0], D_1) → D'_1
  108. Vector(D, D'_1) → v_1
  109. Translate(p_2, v_1) → q_2
  110. Angle(E, D_1, D) → ε
  111. Rotate(q_2, If[4.5 < d ≤ 5.5, ((d - 4.5) * (π - ε)), π - ε], D_1) → r_2
  112. Intersect(c_2, g'') → K_1, L_1
  113. CircleSector(D, K_1, I_1) → s_2
  114. Polygon(D, C'', D_1) → poly5, d_5, d_6, c''_1
  115. Dilate(D, If[6 < d ≤ 7, 7 - d, 0], D_1) → D'_2
  116. Vector(D, D'_2) → w_1
  117. Translate(s_2, w_1) → t_2
  118. Angle(D, D_1, C'') → ζ
  119. Rotate(t_2, If[7 < d ≤ 8, ((-(d - 7)) * (π - ζ)), (-(π - ζ))], D_1) → c_3
  120. Dilate(E, If[8.5 < d ≤ 9.5, 9.5 - d, 0], C'') → E'
  121. Segment(E, E') → l_2
  122. Segment(E, C'') → m_2
  123. Polygon(A, C, F) → poly6, f_3, a_2, c_4
  124. Polygon(D, C'', E) → poly7, e_4, d_7, c''_2