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梯形的性质 by Alfred Estberg

梯形的性质 by Alfred Estberg
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2014-11-12 01:02
多边形变换几何作图
这个范例演示了梯形的性质。涉及的核心数学概念包括几何作图、变换和多边形。通过使用GeoGebra命令如Segment、Polygon、Mirror和Rotate，可以构造梯形并观察其性质。适合初中及以上学生学习几何作图和变换。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Line(D, a) → b
  3. Point(b) → C
  4. Polygon(A, B, C, D) → poly1, a_1, b_1, c, d
  5. Segment(A, C) → e
  6. Segment(B, D) → f
  7. Mirror(B, e) → B'
  8. Circle(B, (Distance[B, B'] * ReflectAC / 10)) → g
  9. Intersect(g, Segment[B, B']) → E, F
  10. Polygon(A, C, E) → poly2, e_1, a_2, c_1
  11. Mirror(A, f) → A'
  12. Circle(A, (Distance[A, A'] * ReflectBD / 10)) → h
  13. Intersect(h, Segment[A, A']) → G, H
  14. Polygon(B, D, G) → poly3, g_1, b_2, d_1
  15. Polygon(A, C, F) → poly4, f_1, a_3, c_2
  16. Intersect(e, f) → I
  17. Rotate(A, α, I) → A'_1
  18. Rotate(B, α, I) → B'_1
  19. Rotate(C, α, I) → C'
  20. Rotate(D, α, I) → D'
  21. Polygon(A'_1, B'_1, C', D') → poly1', a'_1, b'_1, c', d'
  22. Segment(A'_1, C') → i
  23. Segment(B'_1, D') → j
  24. OrthogonalLine(D, c) → k
  25. OrthogonalLine(C, c) → l
  26. Intersect(k, a_1) → J
  27. Intersect(l, a_1) → K
  28. Segment(J, K) → m
  29. Intersect(((-(x(Line[D, C]) / y(Line[D, C]))) * x) - z(Line[D, C]) / y(Line[D, C]), c, 1) → O
  30. OrthogonalLine(D, c) → n
  31. OrthogonalLine(C, c) → p
  32. Intersect(n, a_1) → L
  33. Intersect(p, a_1) → M
  34. Segment(L, M) → q
  35. Point(Segment[L, M]) → N
  36. OrthogonalLine(N, a_1) → r
  37. Intersect(r, c) → P
  38. Ray(A, B) → s
  39. Ray(D, C) → t
  40. Circle(A, ((2 * ReflectPerp) * Segment[A, N])) → h_1
  41. Intersect(h_1, s) → Q, S
  42. Circle(D, ((2 * ReflectPerp) * Segment[D, P])) → d_2
  43. Intersect(d_2, t) → R, T
  44. Polygon(P, R, Q, N) → q1, p_2, r_3, q_2, n_2
  45. Polygon(P, T, S, N) → q2, p_3, t_3, s_3, n_3