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Constructing an Isosceles Trapezoid by FLINK-Team (2)

Constructing an Isosceles Trapezoid by FLINK-Team (2)
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2023-06-16 16:08
PolygonAngleGeometric Construction
In collections Deltoid - Eigenschaften und Konstruktionen
This example demonstrates how to construct an isosceles trapezoid using compass and straightedge. Key mathematical concepts include symmetry, compass construction, and geometric transformations. The construction steps involve determining the axis of symmetry, using compass to set lengths, and completing the figure through geometric transformations. Suitable for middle and high school students learning geometric construction skills, both for classroom instruction and independent practice.

GeoGebra Commands & Parameters

  1. Midpoint(MaschaB, MaschaD) → I
  2. Segment(MaschaB, MaschaD) → MaschaDia2
  3. OrthogonalLine(I, MaschaDia2) → f
  4. Circle(MaschaB, (SeiteAListe(modus) * skala)) → c
  5. Intersect(c, f) → J, MaschaA
  6. SpeechBubbleRight(SpeechMascha, 8, 2) → SpeechBubbleMascha
  7. Segment(SkizzeE3, SkizzeE1) → SkizzeDia1
  8. Mirror(SkizzeE2, SkizzeDia1) → SkizzeE4
  9. Segment(SkizzeE2, SkizzeE4) → SkizzeDia2
  10. Segment(SkizzeE2, SkizzeE3) → SkizzeSeite1
  11. Segment(SkizzeE3, SkizzeE4) → SkizzeSeite2
  12. Segment(SkizzeE4, SkizzeE1) → SkizzeSeite3
  13. Segment(SkizzeE1, SkizzeE2) → SkizzeSeite4
  14. Rotate(MaschaB + (-0.6, 0), animGeoM, I) → GeoL
  15. Mirror(GeoL, I) → GeoR
  16. Circle(MaschaA, (DiagonaleEListe(modus) * skala)) → d
  17. Intersect(d, f) → MaschaC, M
  18. Point(f) → MaschaSymmE1
  19. Point(f) → MaschaSymmE2
  20. Segment(MaschaSymmE1, MaschaSymmE2) → g
  21. Angle(MaschaSymmE1, I, MaschaB) → HelpW
  22. Point(c) → BogenHelp1
  23. Point(c) → BogenHelp2
  24. CircleArc(MaschaB, BogenHelp2, BogenHelp1) → Bogen1
  25. Point(d) → BogenHelp3
  26. Mirror(BogenHelp3, g) → BogenHelp4
  27. CircleArc(MaschaA, BogenHelp3, BogenHelp4) → Bogen5
  28. Polygon(MaschaA, MaschaB, MaschaC, MaschaD) → v1, maschaa, maschab, maschac, maschad
  29. Angle(MaschaB, MaschaA, MaschaD) → α
  30. Angle(MaschaA, MaschaD, MaschaC) → δ
  31. Angle(MaschaD, MaschaC, MaschaB) → γ
  32. Angle(MaschaC, MaschaB, MaschaA) → β
  33. Mirror(BogenHelp1, f) → BogenHelp1'
  34. Mirror(BogenHelp2, f) → BogenHelp2'
  35. CircleArc(MaschaD, BogenHelp1', BogenHelp2') → Bogen2
  36. Circle(MaschaA, (skala * 4)) → h
  37. Point(h) → BogenHelp5
  38. Mirror(BogenHelp5, f) → BogenHelp6
  39. CircleArc(MaschaA, BogenHelp5, BogenHelp6) → Bogen3
  40. Circle(MaschaC, (skala * 5)) → k
  41. Point(k) → BogenHelp7
  42. Mirror(BogenHelp7, f) → BogenHelp8
  43. CircleArc(MaschaC, BogenHelp8, BogenHelp7) → Bogen4
  44. Angle(SkizzeE4, SkizzeE3, SkizzeE2) → ε
  45. Segment(MaschaC, MaschaA) → MaschaDia1
  46. Segment(MaschaB, MaschaD) → j
  47. CircleArc(MaschaB, BogenHelp2, BogenHelp1) → Bogen1Grau
  48. CircleArc(MaschaD, BogenHelp1', BogenHelp2') → Bogen2Grau
  49. CircleArc(MaschaA, BogenHelp5, BogenHelp6) → Bogen3Grau
  50. CircleArc(MaschaC, BogenHelp8, BogenHelp7) → Bogen4Grau
  51. CircleArc(MaschaA, BogenHelp3, BogenHelp4) → Bogen5Grau
  52. Midpoint(MaschaB, MaschaD) → MaschaM
  53. Angle(MaschaA, MaschaM, MaschaB) → ζ
  54. Segment(B_1, MaschaC) → l
  55. Segment(C_1, MaschaC) → m
  56. Circle(MaschaC, MaschaB) → e
  57. Point(e) → D_1
  58. Mirror(D_1, m) → E_1
  59. Mirror(D_1, Segment[MaschaC, MaschaC + (0, 1)]) → F_1
  60. Mirror(F_1, l) → G_1
  61. CircleArc(MaschaC, F_1, G_1) → p
  62. CircleArc(MaschaC, E_1, D_1) → q
  63. Circle(MaschaB, MaschaD + (-0.5, 0)) → HelperCirc
  64. Point(HelperCirc) → A_1
  65. Point(HelperCirc) → H_1
  66. Point(HelperCirc) → I_1
  67. Point(HelperCirc) → J_1
  68. CircleArc(MaschaB, H_1, A_1) → BogenSymm2
  69. CircleArc(MaschaB, I_1, J_1) → BogenSymm1
  70. Mirror(BogenSymm2, g) → BogenSymm2'
  71. Mirror(BogenSymm1, g) → BogenSymm1'
  72. Segment(MaschaB, MaschaD) → MaschiaDia2Mascha

AI Drawing Prompt Reference

Draw an isosceles trapezoid by first defining the base AB, then drawing a circle with center A and radius 1.5 times the base length, intersecting the perpendicular line at point C. Next, draw a circle with center B and the same radius, intersecting the perpendicular line at point D. Connect AD and BC to form the isosceles trapezoid ABCD. Note that angles α, δ, γ, β are at the corners of the trapezoid, with AD equal to BC and AB parallel to CD.
The prompt above was compiled from the original drawing commands and is for reference only.