积极 AI Logo 积极 AI

平行四边形面积公式探索

平行四边形面积公式探索
几何画板及绘图内容加载中，请稍等……
2014-07-01 20:27
多边形向量几何作图
①本范例通过交互式演示，帮助学习者直观理解平行四边形面积公式的推导过程；②涉及的核心数学概念包括平行四边形、底边、高、向量、几何变换；③作图要点提炼自 GeoGebra 命令：Intersect, Polygon, Point, Segment, Line, Midpoint, Min, OrthogonalLine, Vector, Translate，对象包括 A, minB, maxB, constrainB, a, b, B, c, maxheight, minheight, constrainheight, d, e, height, f, constrainC, g, h, C, i, j, D, poly1, a_1, b_1, c_1, d_1, base_1, base_2, m_1, m_2, m_3, m_4, m_5, base_3, text1, text2, vheight_1, vheight_2, vheight_3；④适合初中及以上学生，用于几何教学和公式理解。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Polygon(A + (minB, 0), A + (maxB, 0)) → constrainB, a, b
  3. Point(constrainB) → B
  4. Segment(A, B) → c
  5. Polygon(A + (0, minheight), A + (0, maxheight)) → constrainheight, d, e
  6. Point(constrainheight) → height
  7. Line(height, c) → f
  8. Polygon((x(B) + (0.5 * x(B - A)), y(height)), (x(B) - (0.5 * x(B - A)), y(height))) → constrainC, g, h
  9. Point(constrainC) → C
  10. Line(C, B) → i
  11. Line(A, i) → j
  12. Intersect(f, j) → D
  13. Polygon(A, B, C, D) → poly1, a_1, b_1, c_1, d_1
  14. Segment(base_1, base_2) → m_1
  15. Segment(base_1, base_1 + (0.5, 0.5)) → m_2
  16. Segment(base_1, base_1 + (0.5, (-0.5))) → m_3
  17. Segment(base_2, base_2 + ((-0.5), 0.5)) → m_4
  18. Segment(base_2, base_2 + ((-0.5), (-0.5))) → m_5
  19. Midpoint(base_1, base_2) → base_3
  20. Midpoint(vheight_1, vheight_2) → vheight_3
  21. Segment(vheight_1, vheight_2) → n_1
  22. Segment(vheight_2, vheight_2 + ((-0.5), (-0.5))) → n_2
  23. Segment(vheight_2, vheight_2 + (0.5, (-0.5))) → n_3
  24. Segment(vheight_1, vheight_1 + ((-0.5), 0.5)) → n_4
  25. Segment(vheight_1, vheight_1 + (0.5, 0.5)) → n_5
  26. Midpoint(vheight_4, vheight_5) → vheight_6
  27. Segment(vheight_4, vheight_5) → p_1
  28. Segment(vheight_5, vheight_5 + (0.5, (-0.5))) → p_2
  29. Segment(vheight_5, vheight_5 + ((-0.5), (-0.5))) → p_3
  30. Segment(vheight_4, vheight_4 + (0.5, 0.5)) → p_4
  31. Segment(vheight_4, vheight_4 + ((-0.5), 0.5)) → p_5
  32. Min(x(A), x(D)) → ADmin
  33. OrthogonalLine(B, f) → k
  34. Intersect(f, k) → E
  35. Polygon(E, C, B) → poly2, b_2, e_1, c_2
  36. Vector(B, A) → t_1
  37. Translate(E, Vector[(rot * t_1)]) → E'
  38. Translate(C, Vector[(rot * t_1)]) → C'
  39. Translate(B, Vector[(rot * t_1)]) → B'
  40. Polygon(E', C', B') → poly2', b', e', c'
  41. Polygon(D, A, B, E) → poly3, d_2, a_2, b_3, e_2
  42. OrthogonalLine(A, f) → l
  43. Intersect(l, f) → F
  44. Polygon(F, A, B, C) → poly4, m, n, p, q
  45. Polygon(D, F, A) → poly5, r, s, t
  46. Vector(A, B) → t_2
  47. Translate(D, Vector[(rot * t_2)]) → D'
  48. Translate(D, Vector[(rot * t_2)]) → D'_1
  49. Translate(F, Vector[(rot * t_2)]) → F'
  50. Translate(A, Vector[(rot * t_2)]) → A'
  51. Polygon(D'_1, F', A') → poly5', a', d'_1, f'

AI 绘图提示语参考

画一个平行四边形，展示其面积公式。首先绘制坐标轴并标记交点，然后创建平行四边形的底边和高度，用向量表示。接着，通过几何变换展示平行四边形与长方形的等积性，包括旋转和平移操作。最后，用不同颜色和线条强调关键部分，如底边、高度和变换后的图形，并标注相关面积公式。
以上提示语为根据原始绘图命令整理而来，仅供参考。