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三角形上的矩形

三角形上的矩形
几何画板及绘图内容加载中，请稍等……
2017-07-27 21:03
测试改名0解析几何概率统计几何作图
①本范例演示在三角形内部构造矩形的动态过程与几何关系；②涉及核心数学概念包括矩形、概率、割线或割线幂、幂函数、最大公约数与最小公倍数、四边形；③作图要点提炼自构造摘要，使用了矩形、线段、垂线、多边形、角平分线、交点、角度、条件语句等GeoGebra命令与对象；④适合高中数学教学，用于探索几何变换与概率统计应用。

GeoGebra 命令及参数

  1. Rectangle1(C, B) → D, E
  2. Rectangle1(A, C) → F, G
  3. Rectangle1(B, A) → H, I
  4. Segment(A, B) → f
  5. Segment(B, C) → g
  6. Segment(C, A) → h
  7. OrthogonalLine(C, g) → k
  8. Polygon(B, D, E, C) → poly1, b, d, e, c
  9. Polygon(C, F, G, A) → poly2, c_1, f_1, g_1, a
  10. Polygon(A, H, I, B) → poly3, a_1, h_1, i, b_1
  11. Segment(F, F + (t6 * (E - F))) → j
  12. LineBisector(j) → n_2
  13. Segment(H, H + (t5 * (G - H))) → l
  14. LineBisector(l) → p
  15. Segment(D, D + (t4 * (I - D))) → m
  16. LineBisector(m) → q
  17. Intersect(q, n_2) → J
  18. Intersect(n_2, j) → K
  19. Intersect(p, l) → L
  20. Intersect(m, q) → M
  21. Angle(F, K, J) → α
  22. Angle(H, L, J) → β
  23. Angle(D, M, J) → γ
  24. Segment(K, E) → r
  25. Segment(K, F) → s
  26. Segment(G, L) → k_1
  27. Segment(L, H) → l_1
  28. Segment(D, M) → m_1
  29. Segment(M, I) → n_1
  30. Segment(D, D + (t4 * (I - D))) → p_1
  31. If(t1 < 1, Segment[B, B + (t1 * (D - B))], If[t1 < 2, Segment[D, D + ((t1 - 1) * (E - D))], Segment[E, E + ((t1 - 2) * (C - E))]]) → q_1
  32. If(t2 < 1, Segment[C, C + (t2 * (F - C))], If[t2 < 2, Segment[F, F + ((t2 - 1) * (G - F))], Segment[G, G + ((t2 - 2) * (A - G))]]) → r_1
  33. If(t3 < 1, Segment[A, A + (t3 * (H - A))], If[t3 < 2, Segment[H, H + ((t3 - 1) * (I - H))], Segment[I, I + ((t3 - 2) * (B - I))]]) → s_1
  34. Segment(K3, K3 + (t7 * (J - K3))) → t
  35. Segment(L3, L3 + (t7 * (J - L3))) → i_1
  36. Segment(M3, M3 + (t7 * (J - M3))) → j_1