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三角形上的正方形与平行四边形 by Doug Kuhlmann

三角形上的正方形与平行四边形 by Doug Kuhlmann
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2017-07-26 22:59
测试改名0多边形
这个范例展示了在三角形上构造正方形和平行四边形的过程。核心概念包括几何构造、多边形和线段。通过使用GeoGebra命令如Polygon、Segment、If等，可以动态地调整三角形的边长，观察正方形和平行四边形的变化。适合初中和高中学生学习几何构造和变换。

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. Intersect(t_1, a_1) → M
  29. Segment(K, K + (t7 * (M - K))) → b_1
  30. Segment(J, J + (t7 * (M - J))) → c_1
  31. Segment(L, L + (t7 * (M - L))) → d_1