菱形(Deltoid)几何构造练习

菱形(Deltoid)几何构造练习
几何画板及绘图内容加载中,请稍等……
2023-06-16 16:09
本范例演示如何用GeoGebra构造菱形(Deltoid)这一特殊四边形。核心数学概念包括菱形的定义、性质(四条边相等、对角线互相垂直平分)以及特殊四边形的分类。作图要点:使用Polygon命令绘制多边形,通过Angle命令测量角度验证菱形性质,利用Segment命令绘制边,用Stretch进行图形变换,结合If条件判断和Textfield文本框实现交互练习。适合5-6年级学生掌握基本几何作图工具(圆规、直尺、量角器或DGS)的使用,培养构造特殊四边形的能力。

GeoGebra 命令及参数

  1. Join(Sequence[Join[{Shuffle[Sequence[1, 7]], Shuffle[Sequence[8, 14]]}], m, 1, 9]) → listExNums
  2. If(Mod[exnum, 7] ≟ 0, 7, Mod[exnum, 7]) → typ
  3. Element({10, 10, 9, 9, 8, 8, 12}, typ) → maxstep
  4. Element({M1, M2, M3, M4, M5, M6, M7, M8, M9, M10, M11, M12, M13, M14}, exnum) → M
  5. Textfield(input1) → InputBox1
  6. Textfield(input2) → InputBox2
  7. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  8. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {7, 5, 7, 7, 4, 0, 2, 5, 9, 8, 0, 9, 4, 7, 5, 2, 7, 10, 5, 0, 2, 10, 1, 3, 2, 8, 10, 4, 1, 7, 6, 6, 3, 5, 1, 6, 10, 9, 3, 5, 2, 1, 5, 1, 7, 8, 7, 2, 2, 10, 5, 9, 7, 5, 5, 6, 10, 8, 0, 3, 2, 9, 5, 0, 2, 7, 2, 0, 1, 8, 5, 3, 6, 0, 5, 4, 4, 9, 6, 1, 10, 4, 5, 8, 5, 1, 5, 0, 8, 0, 1, 3, 2, 2, 7, 4, 6, 0, 1, 1}
  9. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  10. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {4, 9, 6, 6, 2, 3, 4, 1, 7, 5, 7, 10, 2, 7, 4, 1, 4, 2, 9, 8, 5, 9, 5, 6, 0, 10, 3, 6, 2, 5, 5, 8, 2, 5, 8, 1, 1, 2, 7, 6, 6, 10, 10, 9, 4, 5, 2, 2, 3, 6, 4, 7, 5, 7, 5, 6, 2, 6, 10, 6, 5, 5, 7, 4, 9, 8, 4, 7, 1, 2, 7, 0, 10, 1, 0, 4, 10, 5, 5, 10, 6, 10, 5, 8, 6, 5, 8, 5, 2, 1, 8, 3, 1, 1, 2, 3, 6, 9, 0, 9}
  11. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  12. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  13. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  14. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  15. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  16. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  17. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  18. Defined((input1 * input2)) → fixed
  19. Angle(B, A, D) → walpha
  20. Angle(C, B, A) → wbeta
  21. LaTeX(typ, true, true) → Text3
  22. Segment(A, B) → a1
  23. Segment(A, D) → a2
  24. Segment(B, C) → b1
  25. Segment(C, D) → b2
  26. Segment(A, M) → eo
  27. Segment(M, C) → eu
  28. Segment(B, D) → f
  29. Zip(If[m < 5, " cm", "°"], m, numValues) → listEH
  30. Angle(A, D, C) → wdelta
  31. Angle(D, C, B) → wgamma
  32. Stretch(A, Line[B, D], 1.2) → A'
  33. Stretch(C, Line[B, D], 1.2) → C'
  34. Segment(A', C') → elang
  35. Stretch(B, Line[A, C], 1.3) → B'
  36. Stretch(D, Line[A, C], 1.3) → D'
  37. Segment(B', D') → flang
  38. Angle(A, M, B) → rechterwinkel
  39. Stretch(B, OrthogonalLine[Midpoint[B, C], Line[B, C]], 1.2) → B'_{1}
  40. Stretch(C, OrthogonalLine[Midpoint[B, C], Line[B, C]], 1.2) → C'_{1}
  41. Segment(B'_{1}, C'_{1}) → b1lang
  42. Stretch(C, OrthogonalLine[Midpoint[C, D], Line[C, D]], 1.2) → C'_{2}
  43. Stretch(D, OrthogonalLine[Midpoint[C, D], Line[C, D]], 1.2) → D'_{1}
  44. Segment(C'_{2}, D'_{1}) → b2lang
  45. Stretch(A, OrthogonalLine[Midpoint[A, D], Line[A, D]], 1.2) → A'_{1}
  46. Stretch(D, OrthogonalLine[Midpoint[A, D], Line[A, D]], 1.2) → D'_{2}
  47. Segment(A'_{1}, D'_{2}) → a2lang
  48. Stretch(A, OrthogonalLine[Midpoint[A, B], Line[A, B]], 1.2) → A'_{2}
  49. Stretch(B, OrthogonalLine[Midpoint[A, B], Line[A, B]], 1.2) → B'_{2}
  50. Segment(A'_{2}, B'_{2}) → a1lang
  51. Element({2, 1, 3, 3, 4, 3, 4}, typ) → numCheckValue
  52. If((checkValue * 10) - floor((checkValue * 10)) ≥ 0.5, (floor((checkValue * 10)) * 0.1) + 0.1, (floor((checkValue * 10)) * 0.1)) → checkValueGerundet
  53. If(step ≟ 1, G_1, G_2) → G
  54. If(step ≟ 1, H_1, H_2) → H
  55. Angle(B, M, C) → rechterwinkel2

AI 绘图提示语参考

画一个风筝形状的图形,四条边长度相等,对角线互相垂直且平分。先绘制一个四边形,确保四条边长度相同,然后用工具测量对角线的交角,验证它们是否为直角。接着,将四边形的一对对角线向外拉伸,使图形变形,同时保持四条边长度不变,观察对角线的变化。最后,在四边形内部绘制两条对角线,并标注它们的交点和关键角度,展示风筝的几何特性。
以上提示语为根据原始绘图命令整理而来,仅供参考。