三角形面积计算 by Ooi Soo Huat

三角形面积计算 by Ooi Soo Huat
几何画板及绘图内容加载中,请稍等……
2017-12-11 15:19
所属专题 Mathematics Form 1
①本范例演示了如何通过 GeoGebra 动态计算三角形的面积;②涉及的核心数学概念包括解析几何、向量、多边形构造及几何作图;③作图要点提炼自构造摘要,使用了 Line, Point, Intersect, Polygon, Vector, Angle 等命令和对象;④适合高中数学教学,用于理解三角形面积公式及动态几何特性。

GeoGebra 命令及参数

  1. Line(A, xAxis) → a
  2. Line(A, yAxis) → b
  3. Point(a) → B
  4. Line(B, b) → c
  5. Point(c) → C
  6. Line(C, a) → d
  7. Point(d) → G
  8. Intersect(b, d) → D
  9. If(NearC ≟ true, C, If[NearD ≟ true, D, G]) → Pm
  10. DynamicCoordinates(G, x(Pm), y(Pm)) → E
  11. Polygon(A, E, B) → poly1, b_1, a_1, e
  12. OrthogonalLine(E, d) → f
  13. Intersect(a, f) → F
  14. Polygon(E, D, A) → poly2, a_2, e_1, d_1
  15. Polygon(E, C, B) → poly3, b_2, e_2, c_1
  16. Polygon(B, F, E) → poly4, e_3, b_3, f_1
  17. Polygon(A, E, F) → poly5, f_2, a_3, e_4
  18. Midpoint(F, A) → H
  19. Midpoint(F, B) → I
  20. Midpoint(A, D) → J
  21. Midpoint(B, C) → K
  22. Midpoint(A, B) → L
  23. Midpoint(D, C) → M
  24. Circle(D, ja) → g
  25. Circle(A, ja) → h
  26. Circle(J, ja) → k
  27. Line(J, K) → i
  28. Intersect(g, d, 1) → N
  29. Circle(K, ja) → p
  30. Intersect(k, b, 2) → O
  31. Intersect(p, c, 2) → P
  32. Intersect(k, b, 1) → Q
  33. Intersect(p, c, 1) → R
  34. Line(O, P) → j
  35. Line(Q, R) → l
  36. Circle(O, ja) → q
  37. Circle(Q, ja) → s
  38. Intersect(q, j, 1) → S
  39. Intersect(s, l, 1) → T
  40. Vector(S, N) → u
  41. Intersect(h, a, 1) → U
  42. Vector(T, U) → v
  43. Circle(C, ja) → r
  44. Intersect(g, b, 2) → V
  45. Intersect(r, c, 2) → W
  46. Circle(M, ja) → t
  47. Intersect(t, d) → Z, A_1
  48. Circle(L, ja) → g_1
  49. Intersect(g_1, a) → B_1, C_1
  50. Line(C_1, A_1) → m
  51. Line(B_1, Z) → n
  52. Circle(A_1, ja) → h_1
  53. Circle(Z, ja) → k_1
  54. Intersect(h_1, m, 2) → D_1
  55. Intersect(k_1, n, 2) → E_1
  56. Vector(D_1, W) → w
  57. Vector(E_1, V) → u_1
  58. If(x(E) < x(D), "c", "d") → Td
  59. Circle(H, ja) → p_1
  60. Intersect(p_1, a) → F_1, G_1
  61. Line(G_1, f) → i_1
  62. Line(F_1, i_1) → j_1
  63. Circle(G_1, ja) → q_1
  64. Circle(F_1, ja) → r_1
  65. Intersect(q_1, i_1, 1) → H_1
  66. Intersect(r_1, j_1, 1) → I_1
  67. Circle(F, ja) → s_1
  68. Intersect(s_1, a) → J_1, K_1
  69. Intersect(h, b, 1) → L_1
  70. Circle(B, ja) → d_2
  71. Intersect(d_2, c, 1) → O_1
  72. Intersect(s_1, f, 1) → M_1
  73. Circle(I, ja) → t_1
  74. Intersect(t_1, a) → N_1, P_1
  75. Line(P_1, c) → l_1
  76. Line(N_1, c) → m_1
  77. Circle(N_1, ja) → c_2
  78. Circle(P_1, ja) → g_2
  79. Intersect(c_2, m_1, 1) → Q_1
  80. Intersect(g_2, l_1, 1) → R_1
  81. If(x(E) < x(C), Vector[Q_1, M_1], Vector[R_1, M_1]) → n_1
  82. If(x(E) < x(C), Vector[R_1, O_1], Vector[Q_1, O_1]) → u_2
  83. If(x(E) > x(D), Vector[H_1, M_1], Vector[I_1, M_1]) → w_1
  84. If(x(E) > x(D), Vector[I_1, L_1], Vector[H_1, L_1]) → v_1
  85. Circle(P, ja) → h_2
  86. Circle(R, ja) → k_2
  87. Intersect(h_2, j, 2) → S_1
  88. Intersect(k_2, l, 2) → T_1
  89. Intersect(r, d, 2) → U_1
  90. Intersect(d_2, a, 2) → V_1
  91. Vector(S_1, U_1) → v_2
  92. Vector(T_1, V_1) → w_2
  93. Angle(A, D, E) → α
  94. Angle(E, B, A) → β
  95. Angle(E, F, B) → γ
  96. Angle(E, C, B) → δ
  97. Angle(B, A, E) → ε
  98. Angle(C, B, A) → ζ
  99. Angle(A, F, E) → η
  100. Angle(A, D, C) → θ
  101. FractionText(0.5) → text7
  102. SelectedIndex(Bahasa) → nn
  103. If(nn ≟ 1, LaTeX["\text{Area of red region = }"], LaTeX["\text{Luas rantau merah = }"]) → Tex1

AI 绘图提示语参考

画一个三角形,动态计算其面积。首先绘制坐标轴并确定三角形的顶点,然后连接顶点形成三角形。接着,通过交点和向量确定关键点,并利用这些点构建多个辅助图形,如正交线、圆和四边形。最后,展示三角形面积的计算过程,包括中点、向量以及辅助图形的运用。
以上提示语为根据原始绘图命令整理而来,仅供参考。