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全等三角形判定条件

全等三角形判定条件
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2017-04-17 17:04
测试改名0角几何作图
①本范例演示了全等三角形的判定条件；②涉及的核心数学概念包括全等三角形判定定理（如SSS、SAS、ASA、AAS）；③作图要点——从下方『构造摘要』提炼用到了Ray（射线）、Point（点）、Segment（线段）、Circle（圆）、CircleArc（圆弧）、Semicircle（半圆）、Angle（角）、Rotate（旋转）、Intersect（交点）等GeoGebra命令/对象；④适合初中及以上学生学习和理解几何证明。

GeoGebra 命令及参数

  1. Ray(P, P_x) → b
  2. Point(b) → P_1
  3. Segment(P, P_1) → e
  4. Point(Circle[Y, 2 * e]) → X
  5. Circle(Y, X) → r
  6. Point(r) → K
  7. Point(r) → J
  8. CircleArc(Y, K, J) → d_1
  9. Ray(Q, Q_x) → c
  10. Point(c) → Q_1
  11. Segment(Q, Q_1) → f
  12. Ray(R, R_x) → d
  13. Point(d) → R_1
  14. Segment(R, R_1) → g
  15. Point(Circle[Z, 2 * g]) → X'
  16. Circle(Z, X') → s
  17. Point(s) → M
  18. Point(s) → L
  19. CircleArc(Z, M, L) → e_1
  20. Point(Circle[C, 2 * g]) → A'
  21. Circle(C, A') → q
  22. Point(q) → I
  23. Point(q) → H
  24. CircleArc(C, H, I) → c_1
  25. Point(Circle[B, 2 * e]) → A
  26. Circle(B, A) → p
  27. Point(p) → G
  28. Point(p) → F
  29. CircleArc(B, F, G) → t
  30. Semicircle(V, O) → k_1
  31. Segment(B, A) → a
  32. Segment(B, C) → h
  33. Segment(C, A') → i
  34. Segment(Y, X) → j
  35. Segment(Y, Z) → k
  36. Segment(Z, X') → l
  37. Segment(N, O) → n
  38. Point(k_1) → S
  39. Angle(O, N, S) → α
  40. Segment(S, N) → a_1
  41. Rotate(C, α, B) → C'
  42. Angle(C, B, C') → β
  43. Ray(B, C') → b_1
  44. Intersect(p, b_1, 1) → T
  45. Segment(T, B) → g_1
  46. Rotate(Z, α, Y) → Z'
  47. Angle(Z, Y, Z') → γ
  48. Ray(Y, Z') → h_1
  49. Intersect(r, h_1, 1) → U
  50. Segment(U, Y) → i_1
  51. Segment(N, V) → j_1
  52. Intersect(c_1, t, 1) → D
  53. Intersect(d_1, e_1, 1) → E
  54. Segment(T, C) → f_1
  55. Segment(U, Z) → l_1
  56. Semicircle(B_1, A_1) → p_1
  57. Segment(B_1, A_1) → m_1
  58. Point(p_1) → C_1
  59. Segment(W, C_1) → n_1
  60. Angle(C_1, W, B_1) → δ
  61. Rotate(B, -δ, C) → B'
  62. Angle(B', C, B) → ε
  63. Rotate(Y, -δ, Z) → Y'
  64. Angle(Y', Z, Y) → ζ
  65. Ray(C, B') → q_1
  66. Ray(Z, Y') → r_1
  67. Point(b_1) → D_1
  68. Point(q_1) → E_1
  69. Point(h_1) → F_1
  70. Point(r_1) → G_1
  71. Segment(D_1, B) → s_1
  72. Segment(E_1, C) → t_1
  73. Segment(F_1, Y) → a_2
  74. Segment(G_1, Z) → b_2
  75. Semicircle(J_1, I_1) → c_2
  76. Segment(J_1, I_1) → d_2
  77. Point(c_2) → K_1
  78. Segment(H_1, K_1) → e_2
  79. Angle(I_1, H_1, K_1) → η
  80. Rotate(B, η, D_1) → B'_1
  81. Angle(B, D_1, B'_1) → θ
  82. Ray(D_1, B'_1) → f_2
  83. Rotate(Y, η, F_1) → Y'_1
  84. Angle(Y, F_1, Y'_1) → ι
  85. Ray(F_1, Y'_1) → g_2
  86. Point(g_2) → L_1
  87. Segment(L_1, F_1) → h_2
  88. Point(f_2) → M_1
  89. Segment(M_1, D_1) → i_2
  90. Rotate(B, 270*°, C) → B'_2
  91. Angle(B'_2, C, B) → κ
  92. Ray(C, B'_2) → j_2
  93. Rotate(Y, 270*°, Z) → Y'_2
  94. Angle(Y'_2, Z, Y) → λ
  95. Ray(Z, Y'_2) → k_2
  96. Point(j_2) → N_1
  97. Segment(N_1, C) → l_2
  98. Point(k_2) → O_1
  99. Segment(O_1, Z) → m_2
  100. Rotate(B, η, A) → B'_3
  101. Angle(B, A, B'_3) → μ
  102. Rotate(Y, η, X) → Y'_3
  103. Angle(Y, X, Y'_3) → ν
  104. Ray(A, B'_3) → n_2
  105. Ray(X, Y'_3) → p_2
  106. Circle(A, C) → q_2
  107. Point(n_2) → S_1
  108. Segment(S_1, A) → r_2
  109. Point(p_2) → T_1
  110. Segment(T_1, X) → s_2
  111. Ray(B, C) → t_2
  112. Ray(Y, Z) → a_3
  113. Point(t_2) → U_1
  114. Point(a_3) → V_1
  115. Segment(B, U_1) → b_3
  116. Segment(Y, V_1) → c_3
  117. Rotate(B, -δ, U_1) → B'_4
  118. Angle(B'_4, U_1, B) → ξ
  119. Rotate(Y, -δ, V_1) → Y'_4
  120. Angle(Y'_4, V_1, Y) → ο
  121. Ray(U_1, B'_4) → d_3
  122. Ray(V_1, Y'_4) → e_3
  123. Intersect(b_1, d_3) → W_1
  124. Segment(W_1, B) → f_3
  125. Segment(W_1, U_1) → g_3
  126. Intersect(h_1, e_3) → Z_1
  127. Segment(Y, Z_1) → h_3
  128. Segment(Z_1, V_1) → i_3
  129. Angle(B, W_1, U_1) → ρ
  130. Angle(Y, Z_1, V_1) → σ

AI 绘图提示语参考

画两个三角形，分别以两条线段为边，用圆和圆弧标示出它们的对应边相等，展示 SSS、SAS、ASA、AAS 几种全等定理的判定条件，并用旋转和角度测量来验证全等性，最后画出旋转后的三角形和对应角，清晰展示全等三角形的构造过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。