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Dynamic Quadrilateral Construction

Dynamic Quadrilateral Construction
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2020-10-08 16:48
PolygonOptimizationGeometric Construction
This example demonstrates the dynamic construction of quadrilaterals by moving points and segments. Key math concepts involved include polygon construction, linear programming or optimization, arithmetic mean, and natural numbers. GeoGebra commands and objects used in the construction are Polygon, If, Segment, Line, Intersect, OrthogonalLine, Point, and Circle. Suitable for high school students to understand quadrilateral properties and geometric construction techniques.

GeoGebra Commands & Parameters

  1. Polygon(QuPo1, QuPo2, QuPo3, QuPo4) → Qu1, QuSeg1, QuSeg2, QuSeg3, QuSeg4
  2. If(ShowChi, IndexOf[SelectedElement[ListQuadTypeC], ListQuadTypeC], IndexOf[SelectedElement[ListQuadTypeE], ListQuadTypeE]) → QuadType
  3. Segment(PaPo1, PaPo2) → PaSeg1
  4. Segment(PaPo1, PaPo3) → PaSeg2
  5. Line(PaPo2, PaSeg2) → PaAuxLine1
  6. Line(PaPo3, PaSeg1) → PaAuxLine2
  7. Intersect(PaAuxLine1, PaAuxLine2) → PaPo4
  8. Segment(PaPo2, PaPo4) → PaSeg3
  9. Segment(PaPo4, PaPo3) → PaSeg4
  10. Segment(RectPo1, RectPo2) → RectSeg1
  11. OrthogonalLine(RectPo1, RectSeg1) → RectAuxLine1
  12. Point(RectAuxLine1) → RectPo3
  13. OrthogonalLine(RectPo2, RectSeg1) → RectAuxLine2
  14. OrthogonalLine(RectPo3, RectAuxLine1) → RectAuxLine3
  15. Intersect(RectAuxLine2, RectAuxLine3) → RectPo4
  16. Segment(RectPo1, RectPo3) → RectSeg2
  17. Segment(RectPo2, RectPo4) → RectSeg4
  18. Segment(RectPo3, RectPo4) → RectSeg3
  19. Segment(RhomPo1, RhomPo2) → RhomSeg1
  20. Circle(RhomPo1, Length[RhomSeg1]) → RhomAuxCir1
  21. Point(RhomAuxCir1) → RhomPo3
  22. Segment(RhomPo1, RhomPo3) → RhomSeg2
  23. Line(RhomPo2, RhomSeg2) → RhomAuxLine1
  24. Line(RhomPo3, RhomSeg1) → RhomAuxLine2
  25. Intersect(RhomAuxLine1, RhomAuxLine2) → RhomPo4
  26. Segment(RhomPo2, RhomPo4) → RhomSeg4
  27. Segment(RhomPo3, RhomPo4) → RhomSeg3
  28. Segment(SqPo1, SqPo2) → SqSeg1
  29. OrthogonalLine(SqPo1, SqSeg1) → SqAuxLine1
  30. Circle(SqPo1, Length[SqSeg1]) → SqAuxCir1
  31. Intersect(SqAuxCir1, SqAuxLine1, 2) → SqPo3
  32. Segment(SqPo3, SqPo1) → SqSeg2
  33. OrthogonalLine(SqPo2, SqSeg1) → SqAuxLine2
  34. OrthogonalLine(SqPo3, SqSeg2) → SqAuxLine3
  35. Intersect(SqAuxLine2, SqAuxLine3) → SqPo4
  36. Segment(SqPo4, SqPo2) → SqSeg4
  37. Segment(SqPo4, SqPo3) → SqSeg3
  38. Line(PaPo1, PaAuxLine1) → PaAuxLine4
  39. Line(PaPo1, PaAuxLine2) → PaAuxLine3
  40. Line(RectPo1, RectAuxLine3) → RectAuxLine4
  41. Line(RhomPo1, RhomAuxLine2) → RhomAuxLine3
  42. Line(RhomPo1, RhomAuxLine1) → RhomAuxLine4
  43. Line(SqPo1, SqAuxLine3) → SqAuxLine4

AI Drawing Prompt Reference

Draw a dynamic quadrilateral construction featuring an arbitrary quadrilateral formed by four connected vertices, and a switchable special quadrilateral (parallelogram, rectangle, rhombus, or square). Additionally, construct a parallelogram via intersection of two auxiliary lines, a rectangle using perpendicular lines, a rhombus using a circle and auxiliary lines, and a square using perpendiculars and a circle. Show all shapes with clear segments and auxiliary lines, with movable vertices to observe changes.
The prompt above was compiled from the original drawing commands and is for reference only.