角平分线与垂线的构造

角平分线与垂线的构造
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2019-04-12 16:03
①本范例演示了如何通过 GeoGebra 构造三角形的角平分线与垂线;②涉及的核心数学概念包括角平分线、垂线、中线、旋转、镜像等;③作图要点——从下方『构造摘要』提炼用到了 LineBisector(角平分线)、Segment(线段)、Rotate(旋转)、Line(直线)、OrthogonalLine(垂线)、Intersect(交点)、Mirror(镜像)、CircleArc(圆弧)、Circle(圆)、Point(点)、Polygon(多边形)、Angle(角)、PointIn(点在...内)、Midpoint(中点)等 GeoGebra 命令/对象;④适合高中数学几何作图教学与学习。

GeoGebra 命令及参数

  1. LineBisector(A, B) → l_4
  2. Segment(A, B) → f
  3. Rotate(B, gam, A) → B'
  4. Line(A, B') → m_4
  5. OrthogonalLine(A, m_4) → n_4
  6. Intersect(l_4, n_4) → Q
  7. Mirror(Q, f) → Q'
  8. CircleArc(Q', B, A) → c_4
  9. Circle((A + B) / 2, B) → c
  10. Point(c_4) → C
  11. Line(C, yAxis) → g
  12. Line(G, F) → h
  13. Intersect(g, h) → E_1
  14. Line(A, B) → i
  15. Intersect(i, g) → G_1
  16. Polygon(G, E_1, G_1, A) → ct1, d, e, g_1, a_1
  17. Polygon(E_1, F, B, G_1) → ct2, e_1, f_1, b_1, g_2
  18. Segment(A, G) → j
  19. Segment(B, F) → k
  20. Line(A, C) → l
  21. Line(C, B) → m
  22. OrthogonalLine(C, l) → n
  23. OrthogonalLine(A, l) → p
  24. OrthogonalLine(C, m) → q
  25. OrthogonalLine(B, m) → r
  26. Polygon(A, C, 4) → mnohoúhelník1, h_1, i_1, j_1, k_1, D, E
  27. Line(E, D) → l_1
  28. OrthogonalLine(B, l) → s
  29. OrthogonalLine(A, m) → t
  30. Intersect(s, l) → H
  31. Intersect(m, t) → I
  32. Intersect(l_1, s) → L
  33. Polygon(A, H, L, E) → ct3, a_2, h_2, l_2, k_2
  34. Polygon(H, C, D, L) → ct4, h_3, c_1, j_2, l_3
  35. Polygon(C, B, 4) → mnohoúhelník2, m_1, n_1, p_1, q_1, M, N
  36. Line(N, M) → r_1
  37. Intersect(t, r_1) → O
  38. Polygon(I, B, M, O) → ct5, i_2, b_2, m_2, o
  39. Polygon(C, I, O, N) → ct6, c_2, i_3, o_1, n_2
  40. Segment(A, H) → s_1
  41. Segment(H, C) → t_1
  42. Segment(C, D) → d_1
  43. Segment(D, L) → f_2
  44. Segment(L, E) → p_2
  45. Segment(E, A) → q_2
  46. Segment(L, H) → r_2
  47. Segment(G_1, E_1) → s_2
  48. Segment(G, E_1) → t_2
  49. Segment(E_1, F) → d_2
  50. Segment(C, I) → e_2
  51. Segment(I, B) → f_3
  52. Segment(B, M) → g_3
  53. Segment(M, O) → j_3
  54. Segment(O, I) → k_3
  55. Segment(N, O) → m_3
  56. Segment(N, C) → n_3
  57. Segment(G_1, A) → p_3
  58. Segment(C, G_1) → q_3
  59. Segment(H, B) → r_3
  60. Segment(A, I) → s_3
  61. Angle(A, C, B) → α
  62. Polygon(A, B, C) → t1, c_3, a_3, b_3
  63. PointIn(ct1) → Bodct1
  64. PointIn(ct6) → Bodct6_1
  65. PointIn(ct6) → Bodct6
  66. Segment(G, F) → t_3
  67. Segment(E, D) → d_3
  68. Segment(N, M) → e_3
  69. Segment(E, B) → f_4
  70. Segment(C, G) → g_4
  71. Segment(D, B) → h_4
  72. Segment(Bodct6, A) → i_4
  73. Segment(A, M) → j_4
  74. Segment(C, F) → k_4
  75. Midpoint(Bodct6, B) → K
  76. Midpoint(L, A) → P
  77. Angle(B, A, B') → β
  78. Polygon(B, A, 4) → mnohoúhelník3, p_4, q_4, r_4, s_4, R, S
  79. Polygon(C, B, 4) → mnohoúhelník4, t_4, a_4, b_4, d_4, T, U
  80. Polygon(A, C, 4) → mnohoúhelník5, e_4, f_5, g_5, h_5, V, W
  81. Polygon(C, B, 4) → mnohoúhelník6, i_5, j_5, k_5, l_5, Z, A_1
  82. Polygon(A, C, 4) → mnohoúhelník7, m_5, n_5, p_5, q_5, B_1, C_1

AI 绘图提示语参考

绘制一个三角形ABC,然后构造角平分线和垂直平分线。首先,构造角平分线AD和BE,接着构造垂直平分线DE。然后,找到三角形的外心Q,构造过Q的圆弧和圆。接着,构造三角形的中线和高,以及与之相关的垂线和交点。最后,根据这些线段和点,构造多个三角形和四边形,包括中点四边形、垂足四边形和外接圆等。
以上提示语为根据原始绘图命令整理而来,仅供参考。