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相似三角形求解

相似三角形求解
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2016-04-04 11:31
测试改名0三角函数几何作图
所属专题 Similar Triangles Review
①本范例演示如何通过 GeoGebra 工具构建并分析相似三角形；②涉及的核心数学概念包括相似三角形的判定与性质、三角函数应用、角度测量、线段比例关系；③作图要点提炼自构造摘要，使用了 Circle（圆）、Point（点）、Ray（射线）、Polygon（多边形）、Intersect（交点）、Line（直线）、Segment（线段）、Angle（角度）、OrthogonalLine（垂线）、Midpoint（中点）等命令与对象；④适合高中数学教学，用于帮助学生直观理解相似三角形的几何性质和解题方法。

GeoGebra 命令及参数

  1. Circle(A, c) → d
  2. Circle(A, b) → e_4
  3. Point(d) → B
  4. Point(e_4) → C
  5. Ray(A, C) → a
  6. Ray(B, C) → f_4
  7. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  8. Circle(C, c' / (c / b)) → k
  9. Intersect(k, a, 1) → D
  10. Line(D, c_1) → m
  11. Intersect(m, f_4) → E
  12. Polygon(C, D, E) → poly2, e_1, c_2, d_1
  13. Segment(C, D) → p_2
  14. Circle(G, i) → q_2
  15. Circle(G, j) → t
  16. Point(q_2) → J
  17. Circle(J, g_3) → f_1
  18. Intersect(t, f_1, 1) → I
  19. Segment(J, G) → g_1
  20. Segment(G, I) → h_1
  21. Segment(I, J) → i_1
  22. Ray(G, J) → j_1
  23. Circle(J, fj) → k_1
  24. Intersect(k_1, j_1, 2) → F
  25. Circle(I, G) → p_1
  26. Intersect(p_1, i_1, 1) → H_1
  27. Circle(F, Radius[p_1]) → q_1
  28. Intersect(q_1, g_1, 1) → I_1
  29. Circle(I_1, Segment[H_1, G]) → r_1
  30. Intersect(q_1, r_1, 2) → K_1
  31. Ray(F, K_1) → l_1
  32. Ray(G, I) → m_1
  33. Intersect(l_1, m_1) → H
  34. Polygon(G, F, H) → poly3, h_2, g_2, f_2
  35. Angle(G, I, J) → α
  36. Angle(H, F, G) → β
  37. Segment(J, F) → h_{4}
  38. Point(h_{4}) → L_1
  39. Segment(F, H) → n_1
  40. Segment(I, H) → s_1
  41. Point(Circle[R, s]) → Q
  42. Segment(R, Q) → t_1
  43. Circle(Q, r) → d_2
  44. Circle(R, q_4) → e_2
  45. Intersect(d_2, e_2, 2) → S
  46. Circle(R, q') → k_2
  47. Ray(Q, S) → a_2
  48. Intersect(k_2, a_2, 1) → P
  49. Polygon(P, R, Q) → poly4, q_3, n_2, r_2
  50. Segment(R, S) → b_2
  51. Angle(R, P, S) → γ
  52. Angle(Q, R, S) → δ
  53. Segment(S, Q) → i_2
  54. Segment(P, S) → j_2
  55. Segment(R, S) → q
  56. Segment(P, S) → p
  57. Circle(M, o) → s_2
  58. Circle(M, n) → t_2
  59. Point(s_2) → N
  60. Segment(M, N) → l_2
  61. OrthogonalLine(N, l_2) → m_2
  62. Intersect(t_2, m_2, 2) → O
  63. Segment(O, M) → a_3
  64. Polygon(M, N, O) → poly5, o_1, u, n_3
  65. Ray(M, N) → b_3
  66. Circle(M, l) → c_3
  67. Point(c_3) → K
  68. OrthogonalLine(K, b_3) → d_3
  69. Intersect(d_3, b_3) → L
  70. Polygon(M, L, K) → poly6, v, w, l_3
  71. Angle(O, N, M) → ε
  72. Angle(M, L, K) → ζ
  73. Segment(L, N) → e_3
  74. Segment(N, O) → f_3
  75. Segment(F, H) → g
  76. Segment(I, H) → f
  77. Segment(C, D) → e
  78. Segment(T, U) → h_3
  79. OrthogonalLine(U, h_3) → i_3
  80. Midpoint(T, U) → V
  81. Circle(U, V) → k_3
  82. Intersect(k_3, i_3, 1) → W
  83. Polygon(T, U, W) → t1, w_1, t_3, u_1
  84. Angle(T, U, W) → η
  85. Angle(T, U, W) → θ
  86. OrthogonalLine(U, u_1) → j_3
  87. Intersect(j_3, u_1) → Z
  88. Segment(U, Z) → h
  89. Angle(U, Z, T) → ι
  90. Segment(U, Z) → m_3