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三角形上的正方形与平行四边形 by Doug Kuhlmann (2)

三角形上的正方形与平行四边形 by Doug Kuhlmann (2)
几何画板及绘图内容加载中，请稍等……
2017-07-27 04:30
测试改名0多边形解析几何立体几何几何作图
本范例演示在三角形上构造正方形和平行四边形的过程。涉及的核心数学概念包括几何作图、解析几何和立体几何。通过使用GeoGebra命令如Polygon、Segment、Line、Intersect等，可以直观地展示这些几何图形的性质和关系。适合初中及以上学生和教师使用。

GeoGebra 命令及参数

  1. Polygon(B, A, 4) → poly3, r, s, t, a, H, I
  2. Segment(A, B) → f
  3. Segment(B, C) → g
  4. Segment(C, A) → h
  5. Polygon(C, B, 4) → poly1, i, j, k, l, D, E
  6. Polygon(A, C, 4) → poly2, m, n_1, p, q, F, G
  7. 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))]]) → e
  8. 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))]]) → f_1
  9. 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))]]) → i_1
  10. 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))]]) → g_1
  11. Line(E, n_1) → b
  12. Line(F, e) → c
  13. Intersect(b, c) → J
  14. Line(H, i_1) → d
  15. Line(G, s) → h_1
  16. Intersect(d, h_1) → K
  17. Line(I, j) → j_1
  18. Line(D, g_1) → k_1
  19. Intersect(k_1, j_1) → L
  20. Segment(E, E + (t4 * (J - E))) → l_1
  21. Segment(F, F + (t4 * (J - F))) → m_1
  22. Segment(G, G + (t5 * (K - G))) → p_1
  23. Segment(H, H + (t5 * (K - H))) → q_1
  24. Segment(I, I + (t6 * (L - I))) → r_1
  25. Segment(D, D + (t6 * (L - D))) → s_1
  26. Ray(L, B) → t_1
  27. Ray(K, A) → a_1
  28. Midpoint(J, C) → N
  29. Midpoint(K, A) → O
  30. Midpoint(L, B) → P
  31. Midpoint(F, A) → Q
  32. Midpoint(H, B) → R
  33. Midpoint(D, C) → S
  34. Segment(P, P + (t7 * (Q - P))) → d_1
  35. Segment(N, N + (t7 * (R - N))) → c_1
  36. Segment(O, O + (t7 * (S - O))) → b_1
  37. Intersect(d_1, c_1) → M