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风筝的性质

风筝的性质
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2014-11-12 00:59
多边形三角函数几何作图
①本范例演示风筝图形的几何性质；②涉及核心数学概念包括多边形、等腰三角形、三角函数等；③作图要点：使用Segment、Mirror、Polygon、OrthogonalLine、Intersect、Point、Circle、Rotate、Midpoint等GeoGebra命令和对象构建风筝及其相关元素；④适合初中及以上学生学习和理解多边形性质及几何作图。

GeoGebra 命令及参数

  1. Segment(A, C) → a
  2. Mirror(B, a) → D
  3. Polygon(A, B, C, D) → poly1, a_1, b_1, c, d
  4. OrthogonalLine(D, a_1) → f_1
  5. Intersect(f_1, a_1) → Q
  6. Point(Segment[Q, B]) → K
  7. Circle(A, ((2 * ReflectPerp) * Segment[A, K])) → s
  8. OrthogonalLine(K, a_1) → r
  9. Intersect(r, c) → R
  10. Mirror(A, r) → A'_2
  11. Intersect(s, Line[A, A'_2]) → M, N
  12. Mirror(D, r) → D'_1
  13. Circle(D, (ReflectPerp * Segment[D, D'_1])) → t
  14. Intersect(t, Line[D, D'_1]) → O, P
  15. Segment(B, D) → b
  16. Intersect(a, b) → E
  17. Circle(B, (Distance[B, D] * ReflectAC / 10)) → e
  18. Intersect(e, b) → F, J
  19. Polygon(A, F, C) → poly2, f, p, q
  20. Mirror(C, Line[B, D]) → C'
  21. Mirror(A, Line[B, D]) → A'
  22. Circle(C, (Distance[C, C'] * ReflectBD / 10)) → g
  23. Intersect(g, Line[A, C], 1) → G
  24. Circle(A, (Distance[A, A'] * ReflectBD / 10)) → h
  25. Intersect(h, Segment[A, A']) → H, I
  26. Polygon(B, H, D, G) → poly3, k, l, m, n
  27. Rotate(A, α, E) → A'_1
  28. Rotate(B, α, E) → B'
  29. Rotate(C, α, E) → C'_1
  30. Rotate(D, α, E) → D'
  31. Polygon(A'_1, B', C'_1, D') → poly1', a'_1, b', c'_1, d'
  32. Segment(A'_1, C'_1) → i
  33. Segment(B', D') → j
  34. Midpoint(D, D'_1) → L
  35. Polygon(R, K, N, P) → q1, g_1, h_1, c_1, d_1
  36. Polygon(A, J, C) → t1, c_2, a_2, j_2