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Geometric Construction Exercise: Constructing Special Quadrilaterals

Geometric Construction Exercise: Constructing Special Quadrilaterals
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2023-11-28 20:53
PolygonCoordinate GeometryGeometric Construction
In collections Trapez - Eigenschaften und Konstruktionen
This example demonstrates how to construct special quadrilaterals using GeoGebra. The key mathematical concepts include geometric construction, intersection of lines and circles, coordinate systems, and polygons. The construction involves using commands like Sequence, Point, Shuffle, Polygon, and objects such as Line, Intersect, Midpoint. It is suitable for students in grades 5-6 for classroom practice or online learning.

GeoGebra Commands & Parameters

  1. Sequence(QE4 + (Vector[QE4, QE3] / 8 * i), i, 1, 7) → GrenzPunkteOben
  2. Sequence(QE1 + (Vector[QE1, QE4] / 8 * i), i, 1, 7) → GrenzPunkteLinks
  3. Sequence(QE2 + (Vector[QE1, QE4] / 8 * i), i, 1, 7) → GrenzPunkteRechts
  4. Sequence(Segment[GrenzPunkteRechts(i), GrenzPunkteLinks(i)], i, 1, 9) → GitterHorizontal
  5. Sequence(QE1 + (Vector[QE1, QE2] / 8 * i), i, 1, 7) → GrenzPunkteUnten
  6. Sequence(Segment[GrenzPunkteOben(i), GrenzPunkteUnten(i)], i, 1, 9) → GitterVertikal
  7. Sequence(Sequence[Intersect[GitterHorizontal(i), GitterVertikal(j)], i, 1, 7], j, 1, 7) → PunkteMengeCoord, {{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7)}, {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7)}, {(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (3, 7)}, {(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (4, 7)}, {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (5, 7)}, {(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6), (6, 7)}, {(7, 1), (7, 2), (7, 3), (7, 4), (7, 5), (7, 6), (7, 7)}}
  8. Point(PunkteMengeCoord) → InputPunkt
  9. Shuffle(Sequence[1, 7]) → HelperX, {7, 3, 4, 2, 1, 6, 5}
  10. Shuffle(Sequence[1, 7]) → HelperY, {5, 7, 2, 4, 6, 1, 3}
  11. Polygon(QE1, QE2, QE3, QE4) → coordsystem, qe1, qe2, qe3, qe4
  12. Textfield(input1) → InputBox1
  13. Textfield(input2) → InputBox2
  14. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  15. Line(Ursprung, HelpP1) → f
  16. Line(Ursprung, HelpP2) → g
  17. Intersect(g, QuadratKanten(2)) → EndXPos
  18. Intersect(g, QuadratKanten(4)) → EndXNeg
  19. Intersect(f, QuadratKanten(1)) → EndYNeg
  20. Intersect(f, QuadratKanten(3)) → EndYPos
  21. Segment(EndYPos, EndYNeg) → yAchsel
  22. Segment(EndXPos, EndXNeg) → xAchsel
  23. Sequence(EndXNeg + (Vector[EndXNeg, EndXPos] * i / 8), i, 1, 7) → AchsenpunkteX
  24. Sequence(EndYNeg + (Vector[EndYNeg, EndYPos] * i / 8), i, 1, 7) → AchsenpunkteY
  25. Sequence(Distance[AchsenpunkteX(i), Ursprung], i, 1, 7) → BeschriftungXAchse
  26. Sequence(Distance[AchsenpunkteY(i), Ursprung], i, 1, 7) → BeschriftungYAchse
  27. Vector(Ursprung, InputPunkt) → OrangeCoords
  28. Segment(NeoA, NeoB) → neoa
  29. Segment(NeoB, NeoC) → neob
  30. Segment(NeoC, NeoD) → neoc
  31. Segment(NeoD, NeoA) → neod
  32. SpeechBubbleRight(A, 4, 3) → Vieleck1
  33. Line(NeoC, neoa) → paraa
  34. Line(NeoB, neoc) → parac
  35. PolyLine({QE1, QE2, QE3}) → EckeRU
  36. Intersect(paraa, EckeRU) → Hintparaa2
  37. PolyLine({QE1, QE4, QE3}) → EckeLO
  38. Intersect(paraa, EckeLO) → Hintparaa1
  39. Intersect(parac, EckeRU) → Hintparac2
  40. Intersect(parac, EckeLO) → Hintparac1
  41. Segment(Hintparaa1, Hintparaa2) → hintparaa
  42. Segment(Hintparac1, Hintparac2) → hintparac
  43. If(gesucht ≟ 1, NeoA, gesucht ≟ 2, NeoB, gesucht ≟ 3, NeoC, gesucht ≟ 4, NeoD) → SolPunkt
  44. Intersect(Segment[NeoA, NeoC], Segment[NeoB, NeoD]) → MittelpunktTrapez
  45. Text(Text4, BeschPosA, false, true, 0, 0) → Text8
  46. Text(Text5, BeschPosB, false, true, 0, 0) → Text9
  47. Text(Text6, BeschPosC, false, true, 0, 0) → Text10
  48. Text(Text7, BeschPosD, false, true, 0, 0) → Text11
  49. Midpoint(NeoD, NeoC) → B
  50. Midpoint(NeoA, NeoB) → C
  51. Text(Text12, B, false, true, 0, 0) → HintParallel1
  52. Text(Text13, C, false, true, 0, 0) → HintParallel2
  53. SpeechBubbleRight(J, 4, 2.4) → Vieleck2
  54. SpeechBubbleRight(K, 9, 2) → Vieleck3
  55. Circle(InputPunkt, 0.25) → c
  56. Segment(L, L + (0, (-LA))) → h

AI Drawing Prompt Reference

Draw a rectangle with four vertices A, B, C, and D, and their diagonals AC and BD. First, determine the four vertices of the rectangle and connect them to form the rectangle. Then, draw the diagonals AC and BD, which will intersect at the center of the rectangle. Finally, label each vertex and the intersection of the diagonals.
The prompt above was compiled from the original drawing commands and is for reference only.