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Dragomir家族的四边形面积练习

Dragomir家族的四边形面积练习
几何画板及绘图内容加载中，请稍等……
2023-09-07 13:39
多边形几何作图滑块动画
所属专题 Deltoid - Flächeninhalt und Umkehraufgaben Deltoid - Flächeninhalt
本范例以「Dragomir和他的家人」为主题，设计互动式练习，让学生通过拖拽和计算掌握特殊四边形的面积公式。涉及的核心数学概念包括：平行四边形面积（底×高）、梯形面积（（上底+下底）×高÷2）、菱形面积（对角线乘积÷2）、风筝形面积（对角线乘积÷2）。构造要点：使用Polygon命令绘制动态四边形，Segment命令绘制辅助线显示高和對角線，Angle命令测量角度验证特殊四边形性质，Textfield和Input命令实现学生答案输入与即时反馈，Shuffle和Element命令实现题目随机抽取。适合5-6年级学生，可用于课堂练习或课后巩固，培养学生应用和论证几何面积公式的能力。

GeoGebra 命令及参数

  1. Join(Sequence[Shuffle[Sequence[m, m, 1, maxexnum]], i, 1, 20]) → listexnums
  2. SelectedIndex(DropDown1) → input3
  3. Polygon(P2, (x(P2a), y(P2)), P2a, (x(P2), y(P2a))) → v4, p2, f, p2a, g
  4. Translate(Polygon[(0, 0), (sizefbx, 0), (sizefbx, sizefby), (0, sizefby)], P1) → v1
  5. Translate(Polygon[(0, 0), (sizefbx, 0), (sizefbx, sizefby), (0, sizefby)], P1 + (sizefbx + abs1, 0)) → v2
  6. Translate(Polygon[(0, 0), (sizefbx, 0), (sizefbx, sizefby), (0, sizefby)], P1 + (2 * (sizefbx + abs1, 0))) → v3
  7. CountIf(m ∈ v1, m, m1) → minv1
  8. CountIf(m ∈ v2, m, m1) → minv2
  9. CountIf(m ∈ v3, m, m1) → minv3
  10. CountIf(m ∈ v4, m, m2) → minv4
  11. Textfield(input1) → InputBox1
  12. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  13. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {5, 1, 4, 3, 10, 2, 9, 2, 4, 1, 0, 2, 9, 4, 0, 2, 1, 4, 3, 6, 0, 1, 3, 5, 9, 3, 8, 9, 6, 6, 10, 0, 9, 2, 9, 9, 5, 1, 6, 5, 7, 1, 6, 1, 1, 6, 5, 8, 2, 8, 3, 8, 10, 9, 4, 8, 7, 4, 8, 2, 4, 8, 0, 6, 1, 0, 7, 8, 1, 2, 9, 7, 1, 9, 4, 0, 7, 9, 5, 5, 7, 6, 0, 8, 3, 3, 10, 7, 8, 4, 2, 3, 4, 8, 1, 5, 5, 5, 6, 5}
  14. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  15. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 8, 4, 5, 9, 8, 7, 4, 4, 3, 10, 2, 1, 4, 2, 9, 7, 1, 1, 0, 2, 6, 5, 8, 9, 0, 0, 7, 3, 0, 1, 2, 9, 6, 7, 2, 7, 10, 7, 7, 5, 0, 4, 2, 4, 5, 2, 5, 2, 0, 4, 1, 9, 7, 4, 1, 4, 10, 3, 0, 7, 0, 10, 2, 5, 6, 5, 7, 1, 10, 9, 8, 10, 5, 0, 2, 0, 8, 7, 1, 10, 8, 8, 7, 3, 3, 9, 6, 4, 3, 3, 7, 4, 6, 5, 4, 5, 5, 3, 6}
  16. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  17. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  18. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  19. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  20. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  21. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  22. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  23. Segment(C1, C3) → lc1
  24. Segment(C2, C4) → lc2
  25. Segment(A1, A3) → la1
  26. Segment(A2, A4) → la2
  27. Segment(B1, B3) → lb1
  28. Segment(B2, B4) → lb2
  29. Translate(Polygon[(0, 0), ((3 * sizefbx) + (2 * abs1) + 1, 0), ((3 * sizefbx) + (2 * abs1) + 1, sizefby - 1), (0, sizefby - 1)], P1 + (-0.5, 0.5)) → fb1
  30. Segment(D1, D3) → ld1
  31. Segment(D2, D4) → ld2
  32. Segment(E1, E3) → le1
  33. Segment(E2, E4) → le2
  34. Segment(F1, F3) → lf1
  35. Segment(F2, F4) → lf2
  36. Segment(G1, G3) → lg1
  37. Segment(G2, G4) → lg2
  38. Segment(D2, D4) → ld3
  39. Segment(E2, E4) → le3
  40. Segment(G2, G4) → lg3
  41. Segment(H1, H1 + (0, -7)) → lh1
  42. Segment(H1 + (-2, -2), H1 + (2, -2)) → lh2
  43. Segment(I1, I1 + (0, -6)) → li1
  44. Segment(I1 + (-1.5, -2.5), I1 + (1.5, -2.5)) → li2
  45. Segment(J1, J1 + (0, -4)) → lj1
  46. Segment(J1 + (-1.5, -1), J1 + (1.5, -1)) → lj2
  47. Textfield(input2) → InputBox2
  48. Textfield(input4h) → Eingabefeld1
  49. Textfield(input5h) → Eingabefeld2
  50. Textfield(input6h) → Eingabefeld3
  51. Element({PosC1, PosC2, PosC3, PosC4, PosC5}, exnum) → PosCorrect
  52. Angle(E4, Intersect[Segment[E1, E3], Segment[E2, E4]], E1) → we1
  53. Angle(F1, Intersect[Segment[F1, F3], Segment[F2, F4]], F2) → wf1
  54. Angle(G1, Intersect[Segment[G1, G3], Segment[G2, G4]], G2) → wg1
  55. Angle(D4, Intersect[Segment[D1, D3], Segment[D2, D4]], D1) → wd1
  56. Angle(A4, Intersect[Segment[A1, A3], Segment[A2, A4]], A1) → wa1
  57. Angle(B4, Intersect[Segment[B1, B3], Segment[B2, B4]], B1) → wb1
  58. Angle(C4, Intersect[Segment[C1, C3], Segment[C2, C4]], C1) → wc1
  59. Angle(H1 + (0, 5), H1 + (0, -2), H1 + (-6, -2)) → wh1
  60. Angle(I1 + (0, 5), I1 + (0, -2.5), I1 + (-6, -2.5)) → wi1
  61. Angle(J1 + (0, 5), J1 + (0, -1), J1 + (-6, -1)) → wj1

AI 绘图提示语参考

画一个四边形，包含两条对角线和两条高。首先画一个四边形，然后画出对角线，接着画出从每个顶点到对边的高。最后，添加一些辅助线，如平行线和垂直线，帮助理解四边形的性质。
以上提示语为根据原始绘图命令整理而来，仅供参考。