平行四边形尺寸演示

平行四边形尺寸演示
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2018-02-26 17:46
①本范例演示平行四边形的几何构造与尺寸关系;②涉及核心概念包括多边形构造、中点、圆弧、线段、旋转、交点、垂线、角度等;③构造过程中运用了Polygon(多边形)、Midpoint(中点)、CircleArc(圆弧)、Segment(线段)、Rotate(旋转)、Intersect(交点)、OrthogonalLine(垂线)、Line(直线)、Point(点)、Angle(角度)等GeoGebra命令与对象;④适合高中数学教学,用于理解平行四边形的性质与作图方法。

GeoGebra 命令及参数

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Midpoint(B, D) → BD
  3. Midpoint(A, C) → F
  4. Midpoint(B, E) → G
  5. CircleArc(B, DD, D) → e
  6. Segment(B, E) → f
  7. Polygon(B, A, C, E) → vierhoek2, b_1, a_1, c_1, e_1
  8. Polygon(B, E, D) → driehoek1, d_1, b_2, e_2
  9. Rotate(B, (((-(s - 1)) * 180))°, e_1) → B'
  10. Rotate(E, (((-(s - 1)) * 180))°, e_1) → E'
  11. Rotate(D, (((-(s - 1)) * 180))°, e_1) → D'
  12. Polygon(B', E', D') → driehoek1', d', b', e'
  13. Polygon(DD, E, B) → driehoek2, b_3, dd, e_3
  14. Segment(G, F) → g
  15. Polygon(G, F, C, E) → vierhoek3, g_1, f_1, c_2, e_4
  16. Polygon(B, A, F, G) → vierhoek4, b_4, a_2, f_2, g_2
  17. Rotate(G, (((-(s - 3)) * 180))°, f_2) → G'
  18. Rotate(F, (((-(s - 3)) * 180))°, f_2) → F'
  19. Rotate(C, (((-(s - 3)) * 180))°, f_2) → C'
  20. Rotate(E, (((-(s - 3)) * 180))°, f_2) → E'_1
  21. Polygon(G', F', C', E'_1) → vierhoek3', g', f', c', e'_1
  22. Polygon(A, F, G, DD) → vierhoek5, a_3, f_3, g_3, dd_1
  23. Segment(FE, F) → i
  24. Polygon(FE, A, F) → driehoek3, f_4, fe, a_4
  25. Rotate(FE, (((-(s - 5)) * 180))°, i) → FE'
  26. Rotate(A, (((-(s - 5)) * 180))°, i) → A'
  27. Rotate(F, (((-(s - 5)) * 180))°, i) → F'_1
  28. Polygon(FE', A', F'_1) → driehoek3', f'_1, fe', a'
  29. Polygon(B, FE, F, G) → vierhoek6, b_5, fe_1, f_5, g_4
  30. Intersect(g_3, i) → H
  31. OrthogonalLine(H, g', xOyPlane) → j
  32. Line(BD, F) → n
  33. Point(n) → K
  34. CircleArc(K, C, A) → p
  35. Polygon(G, H, F) → driehoek4, f_6, g_5, h_1
  36. Intersect(f_6, Line[FE, GG]) → J
  37. OrthogonalLine(H, b) → k
  38. Intersect(f_5, k) → I
  39. Polygon(G, H, I) → driehoek5, i_1, g_6, h_2
  40. Polygon(FE, F, L) → driehoek6, l, fe_2, f_7
  41. Intersect(f_6, f_7) → M
  42. Segment(G, M) → m
  43. Segment(H, M) → q
  44. Segment(B, D) → r
  45. Angle(A, B, E) → α
  46. Angle(G, F, FE) → β
  47. Segment(D, C) → t
  48. Segment(A, C) → j_1
  49. Segment(A, FE) → k_1
  50. Segment(G, BD) → l_1
  51. Segment(G, BD) → m_1
  52. Segment(G, E) → n_1
  53. CircleArc(F, FA, A) → h

AI 绘图提示语参考

绘制一个平行四边形,包含点A、B、C、D和E。首先画出四边形ABCD,然后找到BD和AC的中点F和G。接着画出以B、D、E为顶点的三角形,以及以B、E、D为顶点的三角形。通过旋转操作,生成新的三角形和四边形。最后,画出平行四边形的对角线,以及与对角线相关的角度和线段。
以上提示语为根据原始绘图命令整理而来,仅供参考。