平行四边形角度

平行四边形角度
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2023-12-06 20:41
这个范例演示了平行四边形的角度特性。核心数学概念包括平行四边形的对角线、角度关系和旋转。使用了GeoGebra命令如Random、Rotate、Angle、Textfield等进行构造。适合5-6年级学生学习特殊四边形的性质。

GeoGebra 命令及参数

  1. Random(1, 360) → randomgrad
  2. Shuffle(Sequence[i, i, 60, 100] \ {90}) → alphaList, {85, 73, 96, 89, 69, 63, 65, 78, 81, 61, 80, 66, 79, 87, 91, 95, 71, 64, 62, 82, 70, 84, 93, 100, 76, 94, 74, 86, 75, 77, 72, 83, 97, 68, 67, 99, 60, 98, 92, 88}
  3. Shuffle(Sequence[minbeta + 40, maxbeta - 30, 10]) → betaList, {100, 90}
  4. Shuffle(2…4) → radlist, {2, 3, 4}
  5. Rotate(MKreis + (0, b), randomgrad°, MKreis) → A
  6. Line(A, MKreis) → j
  7. Rotate(SenkP, (-(α / 2)) + randomgrad°, A) → SenkP'_{1}
  8. Ray(A, SenkP'_{1}) → f
  9. Circle(A, rad1) → c
  10. Intersect(c, f) → B,
  11. Rotate(A, (-β), B) → B'
  12. Ray(B, B') → i
  13. Shuffle({1, 2, 3, 4}) → gesuchtListe, {4, 2, 3, 1}
  14. If(questionCount ≟ 1, 1, questionCount ≟ 2, 2, gesuchtListe(1)) → gesucht
  15. Rotate(SenkP, α / 2 + randomgrad°, A) → SenkP'
  16. Ray(A, SenkP') → g
  17. Shuffle(2…4) → radlist2, {4, 2, 3}
  18. Circle(A, rad2) → p
  19. Intersect(p, g) → D,
  20. Angle(B, A, D) → alp
  21. Rotate(A, β, D) → A'
  22. Ray(D, A') → h
  23. Circle(B, rad2) → e
  24. Intersect(e, i) → F,
  25. Angle(D, C, B) → gam
  26. Textfield(input1) → InputBox1
  27. Textfield(input2) → InputBox2
  28. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  29. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {4, 7, 0, 0, 2, 9, 5, 9, 9, 3, 7, 3, 6, 3, 10, 6, 0, 6, 10, 10, 5, 8, 9, 6, 7, 9, 6, 3, 5, 7, 8, 10, 3, 9, 5, 0, 8, 2, 0, 0, 9, 8, 4, 0, 9, 7, 10, 2, 1, 1, 0, 5, 5, 1, 5, 9, 10, 2, 9, 6, 5, 2, 2, 1, 6, 6, 7, 5, 7, 8, 6, 3, 7, 2, 9, 3, 0, 3, 5, 0, 5, 4, 4, 1, 7, 1, 1, 7, 2, 1, 1, 2, 2, 1, 2, 1, 0, 2, 2, 4}
  30. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  31. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {9, 7, 1, 0, 4, 5, 2, 8, 2, 2, 7, 0, 3, 9, 2, 9, 9, 0, 9, 1, 8, 10, 9, 5, 8, 6, 6, 8, 2, 0, 7, 0, 3, 10, 9, 3, 10, 6, 6, 3, 7, 4, 9, 10, 5, 9, 0, 3, 9, 7, 7, 10, 10, 6, 9, 5, 8, 4, 2, 7, 1, 3, 10, 0, 2, 4, 0, 10, 0, 10, 10, 8, 9, 2, 8, 2, 6, 4, 8, 7, 0, 10, 7, 2, 9, 7, 9, 0, 5, 6, 7, 7, 3, 1, 5, 6, 4, 8, 3, 7}
  32. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  33. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  34. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  35. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  36. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  37. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  38. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  39. Defined(input1) → fixed
  40. Angle(SenkP, A, SenkP') → SantasLittleHelper2
  41. Angle(SenkP'_{1}, A, SenkP) → SantasLittleHelper1
  42. Angle(A, D, C) → del
  43. Angle(C, B, A) → bet
  44. If(questionCount ≟ 1, 2, questionCount ≟ 2, 4, gesucht ≟ 1 ∨ gesucht ≟ 3, RandomElement[{2, 4}], gesucht ≟ 2, RandomElement[{1, 3, 4}], gesucht ≟ 4, RandomElement[{1, 2, 3}]) → gesucht2
  45. Midpoint(A, C) → E
  46. Circle(MKreis, 4) → d
  47. Rotate(A + (0, 0.65), randomgrad°, A) → BeschPosA
  48. Rotate(C + (0, -0.65), randomgrad°, C) → BeschPosC
  49. Rotate(B + (-0.65, 0), randomgrad°, B) → BeschPosB
  50. Rotate(D + (0.65, 0), randomgrad°, D) → BeschPosD
  51. Midpoint(B, D) → MDelt
  52. Text(BeschriftungAlpha, BeschPosAlpha, false, true, 0, 0) → Text10
  53. Text(BeschriftungBeta, BeschPosBeta, false, true, 0, 0) → Text11
  54. Text(BeschriftungGamma, BeschPosGamma, false, true, 0, 0) → Text12
  55. Text(BeschriftungDelta, BeschPosDelta, false, true, 0, 0) → Text13
  56. Text(BeschA, BeschPosA, false, true, 0, 0) → Text14
  57. Text(BeschB, BeschPosB, false, true, 0, 0) → Text15
  58. Text(BeschC, BeschPosC, false, true, 0, 0) → Text16
  59. Text(BeschD, BeschPosD, false, true, 0, 0) → Text17
  60. Segment(A, B) → k
  61. Segment(B, C) → l

AI 绘图提示语参考

画一个平行四边形,展示其对角线、内角关系和旋转特性。首先绘制一个随机角度的平行四边形,然后画出两条对角线,并标示出对角线交点。接着,通过旋转其中一个角,演示平行四边形的旋转对称性,并标出旋转角度。最后,添加文本说明,解释平行四边形的对角线互相平分、对角相等、邻角互补等性质。
以上提示语为根据原始绘图命令整理而来,仅供参考。