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LR7-03-XT3 (Diagonals of a Kite)

LR7-03-XT3 (Diagonals of a Kite)
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2019-05-31 03:46
PolygonAngleTransformationGeometric ConstructionSlider Animation
①This GeoGebra example dynamically demonstrates the properties of the diagonals of a kite, including that the diagonals are perpendicular and one diagonal bisects the other. ②Core mathematical concepts include quadrilateral classification, kite definition, diagonal properties, symmetry, and geometric constructions involving intersections, midpoints, and perpendicularity. ③Construction highlights: from the summary, commands such as Polygon, PointIn, Mirror, Circle, Point, Intersect, If, Segment, LaTeX, Midpoint, Angle, Line, and AreParallel are used to build the kite, auxiliary circles, rhombi, squares, and selectors to switch between different quadrilateral shapes, allowing dynamic exploration of diagonal relationships. ④Suitable for middle school geometry, particularly for grades 8-9 when learning quadrilateral properties, geometric proofs, and dynamic exploration; also useful for teacher demonstrations or student self-study.

GeoGebra Commands & Parameters

  1. Polygon({(-6, 19), (26, 19), (26, 0), (-6, 0)}) → viewBox
  2. PointIn(viewBox) → sqA
  3. PointIn(viewBox) → sqB
  4. Mirror(sqA, AngularBisector[Line[sqA, sqB], OrthogonalLine[sqB, Line[sqA, sqB]]]) → sqC
  5. PointIn(viewBox) → kiteA
  6. PointIn(viewBox) → kiteC
  7. PointIn(viewBox) → rhomB
  8. PointIn(viewBox) → rhomA
  9. Circle(rhomB, rhomA) → circle1forRhombus
  10. Point(circle1forRhombus) → rhomC
  11. Mirror(rhomB, Line[rhomA, rhomC]) → rhomD
  12. Intersect(Line[sqA, Line[sqB, sqC]], Line[sqC, Line[sqA, sqB]]) → sqD
  13. If(showKite, kiteC, If[showRhombus, rhomC, sqC]) → C
  14. If(showKite, kiteA, If[showRhombus, rhomA, sqA]) → A
  15. Segment(A, C) → AC
  16. Circle(Midpoint[AC], kiteA) → circle1forKite
  17. PointIn(circle1forKite) → kiteB
  18. Polygon({(-11.5, 9), (-9, 7.5), (-11.5, 6), (-14, 7.5)}) → selectorShapeRhombus
  19. Mirror(kiteB, Line[kiteA, kiteC]) → kiteD
  20. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  21. Polygon({(-8, 7.5), (-11.5, 11), (-19, 7.5), (-11.5, 4)}) → selectorShapeKite
  22. Polygon({(-19.5, 19.5), (-7.5, 19.5), (-7.5, 3.5), (-19.5, 3.5)}) → selectorBoxQuadrilateral
  23. Polygon({(-12, 8), (-12, 7), (-11, 7), (-11, 8)}) → selectorShapeSquare
  24. Polygon({Vertex[selectorShapeRhombus]}) → selectorBorderRhombus
  25. Polygon({Vertex[selectorShapeKite]}) → selectorBorderKite
  26. Polygon({Vertex[selectorShapeSquare]}) → selectorBorderSquare
  27. If(showKite, kiteD, If[showRhombus, rhomD, sqD]) → D
  28. If(showKite, kiteB, If[showRhombus, rhomB, sqB]) → B
  29. Segment(A, B) → AB
  30. Segment(A, D) → AD
  31. Segment(B, C) → BC
  32. Segment(D, B) → DB
  33. Segment(D, C) → DC
  34. Midpoint(AB) → midAB
  35. Midpoint(AD) → midAD
  36. Midpoint(BC) → midBC
  37. Midpoint(D, C) → midDC
  38. Segment(A, Midpoint[Segment[midAB, B]]) → AB_1
  39. Segment(Midpoint[Segment[midAB, A]], B) → AB_2
  40. Segment(Midpoint[Segment[midAD, D]], A) → AD_1
  41. Segment(Midpoint[Segment[midAD, A]], D) → AD_2
  42. Segment(Midpoint[Segment[midBC, C]], B) → BC_1
  43. Segment(Midpoint[Segment[midBC, B]], C) → BC_2
  44. Segment(D, Midpoint[Segment[midDC, C]]) → DC_1
  45. Segment(Midpoint[Segment[midDC, D]], C) → DC_2
  46. Polygon({A, B, C, D}) → quadrilateral
  47. Intersect(AC, DB) → E
  48. Angle(A, B, C) → ABC
  49. Angle(B, C, D) → BCD
  50. Angle(C, D, A) → CDA
  51. Angle(D, A, B) → DAB
  52. Line(A, B) → lineTop
  53. Line(A, D) → lineLeft
  54. Line(D, C) → lineBottom
  55. Line(B, C) → lineRight
  56. AreParallel(lineLeft, lineRight) → parallelLeftRight
  57. AreParallel(lineTop, lineBottom) → parallelTopBottom
  58. LaTeX(UnicodeToLetter[10003]) → cmark
  59. LaTeX(UnicodeToLetter[10007]) → xmark
  60. LaTeX(Distance[A, E]) → labelAE
  61. LaTeX(Distance[B, E]) → labelBE
  62. LaTeX(Distance[C, E]) → labelCE
  63. LaTeX(Distance[D, E]) → labelDE
  64. Angle(A, E, D) → AED