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任意三角形的面积

任意三角形的面积
几何画板及绘图内容加载中，请稍等……
2020-07-05 05:39
测试改名0向量几何作图
这个范例演示了如何通过几何变换和构造来计算任意三角形（钝角或锐角）的面积。核心数学概念包括几何变换、向量和三角形面积公式。通过使用GeoGebra命令如Line, Segment, OrthogonalLine, Intersect等，可以构造出三角形并进行面积计算。适合初中及以上学生学习几何变换和面积计算。

GeoGebra 命令及参数

  1. Line(A, B) → i
  2. Segment(A, B) → a
  3. Line(C, a) → b
  4. OrthogonalLine(C, b) → e
  5. OrthogonalLine(A, a) → c
  6. OrthogonalLine(B, a) → d
  7. Intersect(b, c) → D
  8. Intersect(d, b) → E
  9. Intersect(e, i) → F
  10. Mirror(F, C) → F'_1
  11. Polygon(F'_1, A, B) → poly1, b_1, f', a_1
  12. Intersect(b_1, b) → G
  13. Intersect(a_1, b) → H
  14. Polygon(D, G, A) → poly2, a_2, d_1, g
  15. Rotate(D, (-(Preuve°)), G) → D'
  16. Rotate(G, (-(Preuve°)), G) → G'
  17. Rotate(A, (-(Preuve°)), G) → A'_1
  18. Polygon(D', G', A'_1) → poly2', a', d', g'
  19. Polygon(H, E, B) → poly3, b_2, h, e_1
  20. Rotate(H, Preuve°, H) → H'
  21. Rotate(E, Preuve°, H) → E'
  22. Rotate(B, Preuve°, H) → B'_1
  23. Polygon(H', E', B'_1) → poly3', b', h', e'
  24. Polygon(G', H', B, A) → poly4, g'_1, h'_1, b_3, a_3
  25. Segment(C, F) → j
  26. Midpoint(I, J) → K
  27. Vector(K, I) → u
  28. Vector(K, J) → v
  29. Segment(A, I) → k
  30. Segment(B, J) → l
  31. Midpoint(j) → L
  32. Vector(A, M) → w
  33. Translate(F'_1, w) → F''_1
  34. Translate(A, w) → A'_2
  35. Translate(B, w) → B'_2
  36. Polygon(F''_1, A'_2, B'_2) → poly1', b'_1, f'', a'_1
  37. Translate(G', w) → G''_1
  38. Translate(H', w) → H''_1
  39. Segment(G''_1, H''_1) → m
  40. Translate(C, w) → C'
  41. Translate(F, w) → F'
  42. Segment(C', F') → j'
  43. Mirror(C', m) → C''
  44. Mirror(F', m) → F''
  45. Segment(C'', F'') → j''
  46. Polygon(F'', G''_1, H''_1) → poly5, h'', f''_1, g''
  47. Translate(G', w) → G''
  48. Translate(H', w) → H''
  49. Translate(B, w) → B'
  50. Translate(A, w) → A'
  51. Polygon(G'', H'', B', A') → poly4', g''_1, h''_1, b'_2, a'_2
  52. Segment(N, O) → n
  53. Segment(P, Q) → p
  54. Polygon(D, E, B, A) → q1, d_2, e_2, b_4, a_4
  55. Polygon(G, H, F'_1) → t1, f'_1, g_1, h_1
  56. Rotate(D, (-(Preuve°)), G) → D'_1
  57. Rotate(E, (-(Preuve°)), G) → E'_1
  58. Rotate(G, (-(Preuve°)), G) → G'_1
  59. Rotate(H, (-(Preuve°)), G) → H'_1
  60. Rotate(F'_1, (-(Preuve°)), G) → R
  61. Polygon(G'_1, H'_1, R) → t1', r, f, q
  62. Polygon(E, H, B) → t2, b_5, e_3, h_2
  63. Translate(E, Vector[(If[Preuve < 180, Preuve / 180, 1] * Vector[E, D])]) → E'_2
  64. Translate(H, Vector[(If[Preuve < 180, Preuve / 180, 1] * Vector[E, D])]) → H'_2
  65. Translate(B, Vector[(If[Preuve < 180, Preuve / 180, 1] * Vector[E, D])]) → B'_3
  66. Polygon(E'_2, H'_2, B'_3) → t2', b'_3, e'_2, h'_2
  67. Polygon(G, E, B, A) → q2, g_2, e_4, b_6, a_5
  68. Segment(G, E) → s
  69. Segment(E, B) → t
  70. Segment(B, A) → f_1
  71. Segment(G, A) → i_1
  72. Intersect(a, b_1) → T
  73. Polygon(D, H, S, T) → q3, d_3, h_3, s_1, t_1
  74. Intersect(b_1, a_1) → U
  75. Intersect(d_3, h_3) → V
  76. Polygon(U, V, G) → t3, g_3, u_1, v_1
  77. Rotate(U, (-(Preuve°)), H) → U'
  78. Rotate(V, (-(Preuve°)), H) → V'
  79. Rotate(G, (-(Preuve°)), H) → G'_2
  80. Polygon(U', V', G'_2) → t3', g'_2, u', v'
  81. Polygon(G, D, A) → t4, a_6, g_4, d_4
  82. Translate(G, Vector[(If[Preuve < 180, Preuve / 180, 1] * Vector[G'_1, G'_2])]) → G'_3
  83. Translate(D, Vector[(If[Preuve < 180, Preuve / 180, 1] * Vector[G'_1, G'_2])]) → D'_2
  84. Translate(A, Vector[(If[Preuve < 180, Preuve / 180, 1] * Vector[G'_1, G'_2])]) → A'_3
  85. Polygon(G'_3, D'_2, A'_3) → t4', a'_3, g'_3, d'_2
  86. Segment(D, E) → j_1
  87. Segment(E, B) → k_1
  88. Segment(D, A) → l_1
  89. Segment(D, G) → m_1
  90. Segment(D, A) → n_1
  91. Vector(C, C + (0.65, 0)) → w_1
  92. Vector(C, C - (0.65, 0)) → c_1
  93. Vector(C, C + (0, 0.65)) → p_1
  94. Vector(C, C - (0, 0.65)) → q_1
  95. Segment(M, F') → r_1
  96. Segment(A, F) → f_2