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Angles Formed by Intersecting Diagonals of Kites and Rectangles

Angles Formed by Intersecting Diagonals of Kites and Rectangles
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2019-04-27 02:05
PolygonAngleVectorGeometric ConstructionSlider Animation
This example demonstrates the angles formed by the diagonals of kites and rectangles. Key mathematical concepts include angle properties and geometric construction. Commands used include Polygon, Flatten, Circle, RemoveUndefined, PointIn, UnitVector, Distance, Sequence, Point, Segment, UnitOrthogonalVector, Intersect, etc. Suitable for middle school and above students to learn about angle properties and geometric construction.

GeoGebra Commands & Parameters

  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