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筝形和矩形对角线交点所形成的角

筝形和矩形对角线交点所形成的角
几何画板及绘图内容加载中，请稍等……
2019-04-27 02:05
多边形角向量几何作图滑块动画
本范例演示了筝形和矩形对角线交点所形成的角。核心数学概念包括角的性质和几何作图。使用了Polygon, Flatten, Circle, RemoveUndefined, PointIn, UnitVector, Distance, Sequence, Point, Segment, UnitOrthogonalVector, Intersect等GeoGebra命令。适合初中及以上学生学习几何作图和角的相关性质。

GeoGebra 命令及参数

  1. Polygon({(left, bottom), (left, top), (-2, top), (-2, bottom)}) → K2Region1
  2. Flatten(Sequence[Sequence[(i, j), i, left, right, 0.5], j, bottom, top, 1]) → gridSpace
  3. Polygon({(left, top), (left, bottom), (right, bottom), (right, top)}) → viewbox
  4. Circle(Kcenter, 2) → KcenterCirc
  5. RemoveUndefined(Zip[If[¬IsInRegion[A, KcenterCirc], A], A, gridSpace]) → K2Region
  6. PointIn(K2Region1) → K2
  7. UnitVector(Vector[K2, Kcenter]) → uMainAxis
  8. Distance(Kcenter, Intersect[Ray[Kcenter, Kcenter + uMainAxis], viewbox]) → K1maxLength
  9. Sequence(Kcenter + (i * uMainAxis), i, 2, K1maxLength, 0.5) → K1Region
  10. Point(K1Region) → K1
  11. Segment(K2, K1) → MainKiteAxis
  12. UnitOrthogonalVector(MainKiteAxis) → uCrossBar
  13. Segment(K2 + UnitVector[Vector[K2, K1]], K1 - UnitVector[Vector[K2, K1]]) → KcenterRegion
  14. Distance(Kcenter, Intersect[Ray[Kcenter, Kcenter + uCrossBar], viewbox]) → K2maxLength
  15. Sequence(Kcenter + (i * uCrossBar), i, 2, K2maxLength, 0.5) → K3Region
  16. PointIn(viewbox) → B
  17. Polygon(C18:C21) → parallelogram
  18. LaTeX((((("\text{\textbf{Question: }" * QUESTION) * "\\\textbf{Instructions: }") * INSTRUCTIONS) * "}")) → allInstruc
  19. PointIn(viewbox) → A12
  20. PointIn(viewbox) → A13
  21. Intersect(Line[A13, v], Line[A12, u]) → A15
  22. Intersect(Line[A13, u], Line[A12, v]) → A14
  23. Segment(A12, A14) → B12
  24. Segment(A12, A15) → B14
  25. Segment(A13, A14) → B13
  26. Segment(A13, A15) → B15
  27. Segment(A12, A13) → D12
  28. Segment(A14, A15) → D13
  29. Intersect(D12, D13) → F12
  30. If(Angle[A12, F12, A14] < 180°, Angle[A12, F12, A14], Angle[A14, F12, A12]) → E12
  31. If(Angle[A15, A13, A14] ≟ 90°, Angle[A15, A13, A14], Angle[A14, A13, A15]) → C13
  32. If(Angle[A14, A12, A15] ≟ 90°, Angle[A14, A12, A15], Angle[A15, A12, A14]) → C12
  33. If(Angle[A13, A14, A12] ≟ 90°, Angle[A13, A14, A12], Angle[A12, A14, A13]) → C14
  34. If(Angle[A12, A15, A13] ≟ 90°, Angle[A12, A15, A13], Angle[A13, A15, A12]) → C15
  35. If(Angle[A14, F12, A13] < 180°, Angle[A14, F12, A13], Angle[A13, F12, A14]) → E13
  36. If(Angle[A13, F12, A15] < 180°, Angle[A13, F12, A15], Angle[A15, F12, A13]) → E14
  37. If(Angle[A15, F12, A12] < 180°, Angle[A15, F12, A12], Angle[A12, F12, A15]) → E15
  38. Element(radioButtonLocations, RECTANGLE) → rb1
  39. Element(radioButtonLocations, KITE) → rb2
  40. Element(radioButtonLocations, showObject) → highlightButton
  41. Segment(Kcenter + (7 * UnitOrthogonalVector[MainKiteAxis]), Kcenter + UnitOrthogonalVector[MainKiteAxis]) → crossSegment
  42. Point(K3Region) → K3
  43. Mirror(K3, MainKiteAxis) → K4
  44. Segment(K3, K1) → Kite1
  45. Segment(K3, K2) → Kite2
  46. Segment(K4, K1) → Kite3
  47. Segment(K4, K2) → Kite4
  48. Polygon(AngleCornerPoints) → AllKiteAngles
  49. Segment(K3, K4) → crossBar
  50. Zip(Text["\textbf{\scalebox{0.8}{90°}}", A + tOffset, true, true], A, AngleCornerPoints) → AllAngleLbls