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Lengths of Diagonals in Rectangles and Rhombi

Lengths of Diagonals in Rectangles and Rhombi
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2019-04-27 03:32
PolygonVectorOptimizationGeometric ConstructionSlider Animation
This example demonstrates the calculation of diagonal lengths in rectangles and rhombi. Key mathematical concepts include geometric construction, vectors, and optimization. Using GeoGebra commands such as Flatten, Circle, and Polygon, users can dynamically adjust the dimensions of rectangles and rhombi to observe changes in diagonal lengths. Suitable for middle school and above students learning geometry and optimization problems.

GeoGebra Commands & Parameters

  1. Flatten(Sequence[Sequence[(i, j), i, left, right, 0.5], j, bottom, top, 1]) → gridSpace
  2. Circle(Rcenter, 2) → RcenterCirc
  3. Polygon({(left, bottom), (left, top), (-1, top), (-1, bottom)}) → R1Region
  4. PointIn(R1Region) → R1
  5. UnitVector(Vector[R1, Rcenter]) → u1
  6. Polygon({(left, top), (left, bottom), (right, bottom), (right, top)}) → viewbox
  7. Segment(R1, R2) → diag1
  8. UnitOrthogonalVector(u1) → u2
  9. Min(Distance[Element[EndPoints, 1], Rcenter], Distance[Element[EndPoints, 2], Rcenter]) → maxLengthR
  10. LaTeX((((("\text{\textbf{Question: }" * QUESTION) * "\\\textbf{Instructions: }") * INSTRUCTIONS) * "}")) → allInstruc
  11. PointIn(viewbox) → A12
  12. PointIn(viewbox) → A13
  13. Intersect(Line[A13, v], Line[A12, u]) → A15
  14. Intersect(Line[A13, u], Line[A12, v]) → A14
  15. Segment(A12, A14) → B12
  16. Segment(A12, A15) → B14
  17. Segment(A13, A14) → B13
  18. Segment(A13, A15) → B15
  19. Segment(A12, A13) → D12
  20. Segment(A14, A15) → D13
  21. If(Angle[A14, A12, A15] ≟ 90°, Angle[A14, A12, A15], Angle[A15, A12, A14]) → C12
  22. If(Angle[A15, A13, A14] ≟ 90°, Angle[A15, A13, A14], Angle[A14, A13, A15]) → C13
  23. If(Angle[A13, A14, A12] ≟ 90°, Angle[A13, A14, A12], Angle[A12, A14, A13]) → C14
  24. If(Angle[A12, A15, A13] ≟ 90°, Angle[A12, A15, A13], Angle[A13, A15, A12]) → C15
  25. Element(radioButtonLocations, RECTANGLE) → rbRectangle
  26. Element(radioButtonLocations, RHOMBUS) → rbRhombus
  27. Element(radioButtonLocations, showObject) → highlightButton
  28. Sequence(Rcenter + (i * u2), i, 2, maxLengthR, 0.5) → R3Region
  29. Point(R3Region) → R3
  30. Mirror(R3, diag1) → R4
  31. Segment(R1, R3) → Rside1
  32. Segment(R3, R2) → Rside2
  33. Segment(R2, R4) → Rside3
  34. Segment(R4, R1) → Rside4
  35. Segment(R3, R4) → diag2
  36. Ray(Rcenter, u2) → rayRcenter