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余弦定理的几何作图与验证

余弦定理的几何作图与验证
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2018-09-23 09:22
测试改名0圆几何作图
本范例通过GeoGebra演示余弦定理在三角形中的应用。核心数学概念包括三角形边角关系、余弦定理公式及几何作图技巧。作图要点涉及使用Circle、Intersect、Polygon等命令构造三角形并验证定理。适合初中生学习几何证明及高中生理解三角函数应用。

GeoGebra 命令及参数

  1. Circle(A_1, 5) → c_4
  2. Intersect(c_4, b_1, 1) → A
  3. Intersect(c_4, b_1, 2) → B
  4. Intersect(c_4, d, 1) → C
  5. Polygon(A, C, B) → poly1, b_2, a_1, c_1
  6. Angle(A, C, B) → α
  7. OrthogonalLine(B, b_2) → e
  8. OrthogonalLine(C, c_1) → f
  9. OrthogonalLine(A, a_1) → g_3
  10. Intersect(e, b_2) → D
  11. Intersect(g_3, a_1) → E
  12. Intersect(f, c_1) → F
  13. Circle(F, c_1) → h_3
  14. Intersect(h_3, f, 2) → G
  15. Segment(F, G) → i
  16. Circle(D, b_2) → k
  17. Intersect(k, e, 2) → H
  18. Segment(D, H) → j
  19. Circle(E, a_1) → p
  20. Intersect(p, g_3, 2) → I
  21. Segment(E, I) → l
  22. Line(H, b_2) → m
  23. Line(G, c_1) → n
  24. Line(I, a_1) → q
  25. Line(C, j) → r
  26. Line(A, j) → s
  27. Line(A, i) → t
  28. Line(B, i) → d_1
  29. Line(B, l) → e_1
  30. Line(C, l) → f_1
  31. Intersect(m, r) → J
  32. Intersect(m, s) → K
  33. Intersect(q, f_1) → L
  34. Intersect(q, e_1) → M
  35. Intersect(n, t) → N
  36. Intersect(n, d_1) → O
  37. Polygon(D, H, J, C) → poly2, d_2, h_1, j_1, c_2
  38. Polygon(C, L, I, E) → poly3, c_3, l_1, i_1, e_2
  39. PointIn(poly2) → Pointpoly2
  40. PointIn(poly3) → Pointpoly3_1
  41. Polygon(A, K, H, D) → poly4, a_2, k_1, h_2, d_3
  42. Polygon(A, F, G, N) → poly5, a_3, f_2, g_1, n_1
  43. PointIn(poly5) → Pointpoly5
  44. PointIn(poly4) → Pointpoly4
  45. Polygon(F, B, O, G) → poly6, f_3, b_3, o, g_2
  46. Polygon(B, M, I, E) → poly7, a_5, m_1, i_2, e_3
  47. PointIn(poly7) → Pointpoly7
  48. PointIn(poly6) → Pointpoly6
  49. PointIn(poly3) → Pointpoly3
  50. Segment(B, D) → p_1
  51. Segment(A, E) → q_1
  52. Segment(F, C) → r_1
  53. Midpoint(h_1) → P
  54. Midpoint(k_1) → Q
  55. Midpoint(g_1) → R
  56. Midpoint(o) → S
  57. Midpoint(l_1) → T
  58. Midpoint(m_1) → U
  59. Segment(P, V) → s_1
  60. Segment(Q, W) → t_1
  61. Segment(R, Z) → j_2
  62. Segment(S, B_1) → k_2
  63. Segment(U, C_1) → l_2
  64. Segment(T, D_1) → m_2
  65. Segment(C, J) → b
  66. Segment(B, M) → a
  67. Segment(A, N) → c