测量:九年级数学_面积:箭头的面积

测量:九年级数学_面积:箭头的面积
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2014-08-02 18:38
①本范例演示如何通过交互式工具探究箭头(作为复合图形)的面积;②涉及的核心数学概念包括面积计算、几何作图、坐标系应用;③作图要点:从构造摘要中提炼,使用了Segment(线段)、Midpoint(中点)、Circle(圆)、Point(点)、Tangent(切线)、Line(直线)、Intersect(交点)、OrthogonalLine(垂线)、Polygon(多边形)、Area(面积)等GeoGebra命令/对象;④适合九年级学生或需要复习复合图形面积计算的学习者使用。

GeoGebra 命令及参数

  1. Segment(B_1, C) → a
  2. Midpoint(a) → D
  3. Circle(D, B_1) → c
  4. Point(a) → E
  5. Circle(D, E) → d
  6. Tangent(B_1, c) → b,
  7. Line(E, b) → e
  8. Line(C, b) → f
  9. Intersect(d, a) → A_1, F
  10. Line(F, b) → g
  11. Point(b) → G
  12. Line(D, b) → i
  13. Point(b) → L
  14. Point(b) → H
  15. Segment(H, G) → h
  16. Point(h) → A
  17. OrthogonalLine(A, h) → k
  18. Point(b) → J
  19. Segment(L, J) → j
  20. Point(j) → B
  21. OrthogonalLine(B, j) → l
  22. Intersect(k, e) → M
  23. Intersect(k, i) → N
  24. Intersect(g, k) → O
  25. Intersect(k, f) → P
  26. Intersect(l, e) → Q
  27. Intersect(l, i) → R
  28. Intersect(l, g) → S
  29. Intersect(l, f) → T
  30. Segment(A, R) → m
  31. Segment(P, R) → n
  32. Segment(A, M) → p
  33. Segment(P, O) → q
  34. Segment(M, E) → r
  35. Segment(E, F) → s
  36. Segment(F, O) → t
  37. Polygon(A, M, E, D, F, O, P, R) → poly1, i_1, m_1, e_1, d_1, f_1, o, p_1, r_1
  38. Polygon(E, B_1, A, M) → Rectangle_1, e_2, b_1, i_2, m_2
  39. Polygon(F, C, P, O) → Rectangle_2, f_2, c_1, p_2, o_1
  40. Polygon(A, N, R, B) → poly4, i_3, n_1, r_2, k_1
  41. Polygon(N, P, T, R) → poly5, n_2, p_3, t_1, r_3
  42. Polygon(R, B, A) → Triangle_3, i_4, r_4, k_2
  43. Polygon(P, R, T) → Triangle_4, t_2, p_4, r_5
  44. Polygon(A, N, R) → Triangle_1, r_6, i_5, n_3
  45. Polygon(N, P, R) → Triangle_2, r_7, n_4, p_5
  46. Point(b) → I
  47. OrthogonalLine(I, b) → a_1
  48. Intersect(e, a_1) → K
  49. Intersect(g, a_1) → U
  50. Intersect(f, a_1) → V
  51. Point(b) → W
  52. OrthogonalLine(W, b) → g_1
  53. Intersect(e, g_1) → Z
  54. Intersect(g, g_1) → C_1
  55. Intersect(f, g_1) → D_1
  56. Segment(W, D_1) → h_1
  57. Segment(I, K) → j_1
  58. Segment(B_1, W) → l_1
  59. Segment(C, D_1) → q_1
  60. Segment(K, U) → s_1
  61. Segment(U, V) → a_2
  62. OrthogonalLine(B_1, b_1) → b_2
  63. Point(b_2) → E_1
  64. OrthogonalLine(E_1, b_2) → c_2
  65. Intersect(c_2, k) → F_1
  66. Point(k) → G_1
  67. OrthogonalLine(G_1, k) → d_2
  68. Intersect(d_2, l) → H_1
  69. Segment(E_1, F_1) → g_2
  70. Segment(G_1, H_1) → h_2
  71. Polygon(E, M, O, F) → Rectangle_3, e_3, m_3, o_2, f_3
  72. OrthogonalLine(R, i_4) → j_2
  73. OrthogonalLine(B, i_4) → l_2
  74. Point(l_2) → I_1
  75. OrthogonalLine(I_1, l_2) → q_2
  76. Intersect(q_2, j_2) → J_1
  77. Segment(I_1, J_1) → s_2
  78. Point(s_2) → K_1
  79. Area(Rectangle_1) → u
  80. Area(Rectangle_3) → v
  81. Area(poly1) → w
  82. Area(Triangle_1) → u_1

AI 绘图提示语参考

画一个箭头形状,首先绘制箭头的底边和顶点,然后以底边中点为圆心画一个圆,再以底边与圆的切点为圆心画另一个圆,连接切点与顶点形成直线,交点处绘制辅助线,最后将所有交点和辅助线构成的封闭区域填充颜色,同时保留部分辅助线,形成箭头轮廓和内部分割区域。
以上提示语为根据原始绘图命令整理而来,仅供参考。