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Diagonals of a Parallelogram Demo

Diagonals of a Parallelogram Demo
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2019-05-29 20:46
VectorGeometric Construction
This example demonstrates the properties of diagonals in a parallelogram, focusing on the intersection point and the relationship between the segments formed. Key math concepts include parallelograms, diagonals, midpoints, angle bisectors, and vectors. GeoGebra commands and objects used in construction are Polygon, PointIn, Intersect, Mirror, Circle, Line, Segment, Midpoint, Angle, and AreParallel. Suitable for middle school and above mathematics education to visually understand geometric properties of parallelograms.

GeoGebra Commands & Parameters

  1. Polygon({(-6, 19), (26, 19), (26, 0), (-6, 0)}) → viewBox
  2. PointIn(viewBox) → paraA
  3. PointIn(viewBox) → paraB
  4. PointIn(viewBox) → recB
  5. PointIn(viewBox) → sqB
  6. PointIn(viewBox) → rhomB
  7. PointIn(viewBox) → recA
  8. Point(OrthogonalLine[recB, Line[recA, recB]]) → recC
  9. Intersect(Line[recA, Line[recB, recC]], Line[recC, Line[recA, recB]]) → recD
  10. PointIn(viewBox) → sqA
  11. Mirror(sqA, AngularBisector[Line[sqA, sqB], OrthogonalLine[sqB, Line[sqA, sqB]]]) → sqC
  12. Intersect(Line[sqA, Line[sqB, sqC]], Line[sqC, Line[sqA, sqB]]) → sqD
  13. PointIn(viewBox) → rhomA
  14. Circle(rhomB, rhomA) → circle1forRhombus
  15. Point(circle1forRhombus) → rhomC
  16. Mirror(rhomB, Line[rhomA, rhomC]) → rhomD
  17. PointIn(viewBox) → paraC
  18. If(showParallelogram, paraC, If[showRectangle, recC, If[showRhombus, rhomC, sqC]]) → C
  19. If(showParallelogram, paraB, If[showRectangle, recB, If[showRhombus, rhomB, sqB]]) → B
  20. Line(B, C) → lineRight
  21. If(showParallelogram, paraA, If[showRectangle, recA, If[showRhombus, rhomA, sqA]]) → A
  22. Line(A, B) → lineTop
  23. Intersect(Line[paraA, lineRight], Line[paraC, lineTop]) → paraD
  24. Segment(A, C) → AC
  25. Polygon({(-11.5, 9), (-9, 7.5), (-11.5, 6), (-14, 7.5)}) → selectorShapeRhombus
  26. Polygon({(-19, 10), (-8, 11), (-8, 5), (-19, 4)}) → selectorShapeParallelogram
  27. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  28. Polygon({(-19.5, 19.5), (-7.5, 19.5), (-7.5, 3.5), (-19.5, 3.5)}) → selectorBoxQuadrilateral
  29. Polygon({(-12, 8), (-12, 7), (-11, 7), (-11, 8)}) → selectorShapeSquare2
  30. Polygon({Vertex[selectorShapeRhombus]}) → selectorBorderRhombus
  31. Polygon({Vertex[selectorShapeParallelogram]}) → selectorBorderParallelogram
  32. Polygon({Vertex[selectorShapeSquare2]}) → selectorBorderSquare2
  33. If(showParallelogram, paraD, If[showRectangle, recD, If[showRhombus, rhomD, sqD]]) → D
  34. Segment(A, B) → AB
  35. Segment(A, D) → AD
  36. Segment(B, C) → BC
  37. Segment(D, B) → DB
  38. Segment(D, C) → DC
  39. Midpoint(AB) → midAB
  40. Midpoint(AD) → midAD
  41. Midpoint(BC) → midBC
  42. Midpoint(D, C) → midDC
  43. Segment(A, Midpoint[Segment[midAB, B]]) → AB_1
  44. Segment(Midpoint[Segment[midAB, A]], B) → AB_2
  45. Segment(Midpoint[Segment[midAD, D]], A) → AD_1
  46. Segment(Midpoint[Segment[midAD, A]], D) → AD_2
  47. Segment(Midpoint[Segment[midBC, C]], B) → BC_1
  48. Segment(Midpoint[Segment[midBC, B]], C) → BC_2
  49. Segment(D, Midpoint[Segment[midDC, C]]) → DC_1
  50. Segment(Midpoint[Segment[midDC, D]], C) → DC_2
  51. Polygon({A, B, C, D}) → quadrilateral
  52. Intersect(AC, DB) → E
  53. Angle(A, B, C) → ABC
  54. Angle(B, C, D) → BCD
  55. Angle(C, D, A) → CDA
  56. Angle(D, A, B) → DAB
  57. Line(A, D) → lineLeft
  58. Line(D, C) → lineBottom
  59. AreParallel(lineLeft, lineRight) → parallelLeftRight
  60. AreParallel(lineTop, lineBottom) → parallelTopBottom
  61. LaTeX(UnicodeToLetter[10003]) → cmark
  62. LaTeX(UnicodeToLetter[10007]) → xmark
  63. LaTeX(Distance[A, E]) → labelAE
  64. LaTeX(Distance[B, E]) → labelBE
  65. LaTeX(Distance[C, E]) → labelCE
  66. LaTeX(Distance[D, E]) → labelDE
  67. Angle(A, E, D) → AED
  68. Polygon({(-18, 5), (-18, 9.5), (-15, 9.5), (-15, 5)}) → selectorShapeRectangle
  69. Polygon({Vertex[selectorShapeRectangle]}) → selectorBorderRectangle
  70. Polygon({(-17, 7), (-17, 8), (-16, 8), (-16, 7)}) → selectorShapeSquare1
  71. Polygon({Vertex[selectorShapeSquare1]}) → selectorBorderSquare1

AI Drawing Prompt Reference

Draw a parallelogram and its diagonals, then find their intersection point. Next, draw a rectangle and a rhombus, and find their diagonal intersection points. Finally, draw the diagonals of each shape and mark the midpoints of each diagonal.
The prompt above was compiled from the original drawing commands and is for reference only.