三角形的对称点

三角形的对称点
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2015-02-23 08:35
①本范例演示了如何在三角形中找到对称点;②涉及的核心数学概念包括对称轴、中点、角平分线、线段、点、镜像、交点等;③作图要点——使用了Polygon(多边形)、Midpoint(中点)、AngularBisector(角平分线)、Segment(线段)、Point(点)、Mirror(镜像)、Intersect(交点)等GeoGebra命令和对象;④适合高中数学教学和几何作图学习。

GeoGebra 命令及参数

  1. Polygon(M, N, O) → poly3, o, m_1, n
  2. Midpoint(m_1) → Midpoint''
  3. Midpoint(o) → Midpoint
  4. Midpoint(n) → Midpoint'
  5. Polygon(P, Q, R) → poly4, r, p, q
  6. Midpoint(r) → S
  7. Midpoint(q) → T
  8. Midpoint(p) → U
  9. AngularBisector(P, R, Q) → c_1
  10. AngularBisector(Q, P, R) → d_1
  11. Segment(Q, T) → Median''
  12. Segment(U, P) → Median
  13. Segment(S, R) → Median'
  14. AngularBisector(P, Q, R) → s
  15. Polygon(J, K, L) → poly2, l_1, j_1, k_1
  16. Point(k_1) → W
  17. Segment(W, K) → j
  18. Point(l_1) → G
  19. Segment(G, L) → k
  20. AngularBisector(J, K, L) → a_1
  21. AngularBisector(J, L, K) → b_1
  22. AngularBisector(K, J, L) → e_1
  23. Mirror(W, a_1) → W'
  24. Mirror(K, a_1) → K'
  25. Segment(W', K') → Symmedian
  26. Mirror(J, e_1) → J'
  27. Mirror(G, b_1) → G'
  28. Mirror(L, b_1) → L'
  29. Segment(G', L') → Symmedian'
  30. Midpoint(j_1) → B_1
  31. Segment(J, B_1) → t
  32. Mirror(J, e_1) → J'_3
  33. Mirror(B_1, e_1) → Z
  34. Segment(J'_3, Z) → Symmedian''
  35. Polygon(J_1, K_1, L_1) → poly2_1, l_2, j_2, k_2
  36. Point(k_2) → W_1
  37. Segment(W_1, K_1) → j_3
  38. Point(l_2) → G_1
  39. Segment(G_1, L_1) → k_3
  40. AngularBisector(J_1, K_1, L_1) → a_3
  41. AngularBisector(J_1, L_1, K_1) → b_2
  42. AngularBisector(K_1, J_1, L_1) → e_2
  43. Mirror(W_1, a_3) → W'_1
  44. Mirror(K_1, a_3) → K'_1
  45. Segment(W'_1, K'_1) → Symmedian_1
  46. Mirror(G_1, b_2) → G'_1
  47. Mirror(L_1, b_2) → L'_1
  48. Segment(G'_1, L'_1) → Symmedian'_1
  49. Midpoint(j_2) → B_2
  50. Segment(J_1, B_2) → t_1
  51. Mirror(J_1, e_2) → J'_4
  52. Mirror(B_2, e_2) → Z_1
  53. Segment(J'_4, Z_1) → t'_1
  54. Intersect(l_2, Symmedian'_1) → H
  55. Intersect(k_2, Symmedian_1) → V
  56. Intersect(j_2, t'_1) → A_1
  57. Segment(K_1, V) → f_1
  58. Segment(J_1, A_1) → g_1
  59. Segment(H, L_1) → h_1
  60. Polygon(J_2, K_2, L_2) → poly2_2, l_3, j_4, k_4
  61. Point(k_4) → W_2
  62. Segment(W_2, K_2) → j_5
  63. Point(l_3) → G_2
  64. Segment(G_2, L_2) → k_5
  65. AngularBisector(J_2, K_2, L_2) → a_2
  66. AngularBisector(J_2, L_2, K_2) → b_3
  67. AngularBisector(K_2, J_2, L_2) → e_3
  68. Mirror(W_2, a_2) → W'_2
  69. Mirror(K_2, a_2) → K'_2
  70. Segment(W'_2, K'_2) → Symmedian_2
  71. Mirror(G_2, b_3) → G'_2
  72. Mirror(L_2, b_3) → L'_2
  73. Segment(G'_2, L'_2) → Symmedian'_2
  74. Midpoint(j_4) → B_3
  75. Segment(J_2, B_3) → t_2
  76. Mirror(J_2, e_3) → J'_1
  77. Mirror(B_3, e_3) → Z_2
  78. Segment(J'_1, Z_2) → t'_2
  79. Intersect(l_3, Symmedian'_2) → H_1
  80. Intersect(k_4, Symmedian_2) → V_1
  81. Intersect(j_4, t'_2) → A_2
  82. Segment(K_2, V_1) → f_2
  83. Segment(J_2, A_2) → g_2
  84. Segment(H_1, L_2) → h_2
  85. Intersect(f_2, g_2) → SYMMEDIANPOINT
  86. Polygon(J_3, K_3, L_3) → poly2_3, l_4, j_6, k_6
  87. Point(k_6) → W_3
  88. Segment(W_3, K_3) → j_7
  89. Point(l_4) → G_3
  90. Segment(G_3, L_3) → k_7
  91. AngularBisector(J_3, K_3, L_3) → a_4
  92. AngularBisector(J_3, L_3, K_3) → b_4
  93. AngularBisector(K_3, J_3, L_3) → e_4
  94. Mirror(W_3, a_4) → W'_3
  95. Mirror(K_3, a_4) → K'_3
  96. Segment(W'_3, K'_3) → Symmedian_3
  97. Mirror(G_3, b_4) → G'_3
  98. Mirror(L_3, b_4) → L'_3
  99. Segment(G'_3, L'_3) → Symmedian'_3
  100. Midpoint(j_6) → B_4
  101. Segment(J_3, B_4) → t_3
  102. Mirror(J_3, e_4) → J'_2
  103. Mirror(B_4, e_4) → Z_3
  104. Segment(J'_2, Z_3) → t'_3
  105. Intersect(l_4, Symmedian'_3) → H_2
  106. Intersect(k_6, Symmedian_3) → V_2
  107. Intersect(j_6, t'_3) → A_3
  108. Segment(K_3, V_2) → f_3
  109. Segment(J_3, A_3) → g_3
  110. Segment(H_2, L_3) → h_3
  111. Intersect(f_3, g_3) → SYMMEDIANPOINT'
  112. Midpoint(l_4) → B
  113. Midpoint(k_6) → C
  114. Midpoint(j_6) → D
  115. Segment(K_3, C) → a
  116. Segment(J_3, D) → b
  117. Segment(B, L_3) → c
  118. Intersect(a, b) → CENTROID

AI 绘图提示语参考

画一个三角形,标出三个顶点,分别求出每条边的中点和角平分线,连接顶点和对应边的中点得到三条中线,再求出每条角平分线与对边的交点,连接顶点和交点得到三条角平分线,最后求出三条中线的交点即三角形的对称点,并画出由对称点与角平分线交点构成的四边形和五边形。
以上提示语为根据原始绘图命令整理而来,仅供参考。