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Constructing an Isosceles Trapezoid by FLINK-Team

Constructing an Isosceles Trapezoid by FLINK-Team
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2023-11-28 20:52
PolygonAngleTrigonometryGeometric Construction
In collections Trapez - Eigenschaften und Konstruktionen
This example demonstrates how to construct an isosceles trapezoid using compass and straightedge. Key math concepts include polygons, angles, and geometric construction. Construction highlights involve GeoGebra commands such as Point, Segment, Rotate, Angle, Circle, CircleArc, Intersect, Line, and Polygon. Suitable for upper elementary or beginner students learning geometric construction techniques.

GeoGebra Commands & Parameters

  1. Point(Circle[PunktA, 6.5]) → PunktB
  2. Segment(PunktA, PunktB) → Seitea
  3. Rotate(PunktB, 40°, PunktA) → PunktB'
  4. Angle(PunktB, PunktA, PunktB') → α
  5. Segment(PunktA, PunktB') → Schenkelalpha1
  6. Rotate(PunktA, -70°, PunktB) → PunktA'
  7. Angle(PunktA', PunktB, PunktA) → β
  8. Segment(PunktA', PunktB) → Schenkelbeta1
  9. Point(Schenkelalpha1) → A
  10. Point(Schenkelbeta1) → C
  11. Circle(PunktA, 3.8) → kreisd
  12. Point(kreisd) → D_{1}
  13. Point(kreisd) → E
  14. CircleArc(PunktA, D_{1}, E) → Bogend
  15. Segment(A, PunktA) → Schenkelalpha2
  16. Segment(C, PunktB) → Schenkelbeta2
  17. Intersect(Bogend, Schenkelalpha2) → PunktD,
  18. Line(PunktD, Seitea) → Parallelec
  19. Point(Parallelec) → G
  20. Segment(PunktD, G) → Streckeparallele
  21. Intersect(Schenkelbeta2, Streckeparallele) → PunktC
  22. Segment(PunktA, PunktD) → Seited
  23. Segment(PunktD, PunktC) → Seitec
  24. Segment(PunktB, PunktC) → Seiteb
  25. Segment((x(PunktA), y(PunktA) + 0.1), (x(PunktA), y(PunktA) - 0.1)) → beiA
  26. Segment((x(PunktB), y(PunktB) + 0.1), (x(PunktB), y(PunktB) - 0.1)) → beiB
  27. Circle(PunktA1, 4.5) → kreisd1
  28. Point(kreisd1) → PunktD1
  29. Rotate(PunktD1, -45°, PunktA1) → PunktD1'
  30. Angle(PunktD1', PunktA1, PunktD1) → γ
  31. Point(Circle[PunktD1, 6]) → B
  32. Segment(PunktD1, B) → Streckenparallele1
  33. Segment(PunktA1, PunktD1) → Seited1
  34. Segment(PunktA1 - (0, 0.15), PunktA1 + (0, 0.15)) → BeiA1
  35. Segment(PunktD1 + (0, -0.15), PunktD1 + (0, 0.15)) → beiD1
  36. Circle(PunktD1, 3.2) → kreisc
  37. Point(kreisc) → F
  38. Point(kreisc) → H
  39. CircleArc(PunktD1, H, F) → Bogenc
  40. Intersect(Bogenc, Streckenparallele1) → PunktC1,
  41. Circle(PunktC1, 3.8) → kreisb
  42. Segment(PunktA1, PunktD1' + (5, 0)) → Seitea1
  43. Intersect(kreisb, Seitea1) → K, PunktB1
  44. Point(kreisb) → I
  45. Point(kreisb) → J
  46. CircleArc(PunktC1, I, J) → Bogenb
  47. Segment(PunktC1, PunktB1) → Seiteb1
  48. Angle(PunktD, PunktC, PunktB) → δ
  49. Angle(PunktA, PunktD, PunktC) → ε
  50. Angle(PunktC1, PunktB1, PunktA1) → ζ
  51. Angle(PunktD1, PunktC1, PunktB1) → η
  52. Angle(PunktA1, PunktD1, PunktC1) → θ
  53. Segment(PunktA1, PunktB1) → SeiteaNeu
  54. Polygon(L, M, N, O) → q1, l, m, n, o
  55. SpeechBubbleRight(PBubble, 6.5, 2.7) → SpeechBubble
  56. Segment(P, Q) → f
  57. Segment(PunktA2, PunktB2) → Seitea2
  58. Segment((3.5, 7.5), (9.5, 7.5)) → Seitec3
  59. Rotate(PunktA2, -40°, PunktB2) → PunktA2'
  60. Angle(PunktB2, PunktA2, PunktA2') → ι
  61. Ray(PunktA2, PunktA2') → h
  62. Point(h) → T
  63. Segment(PunktA2, T) → Seited2
  64. Intersect(Seited2, Seitec3) → R
  65. Rotate(PunktA2, -60°, PunktB2) → PunktA2'_{1}
  66. Angle(PunktA2, PunktB2, PunktA2'_{1}) → κ
  67. Segment(PunktB2, PunktA2'_{1}) → Seiteb2
  68. Angle(PunktA2'_{1}, PunktB2, PunktA2) → λ
  69. Intersect(Seitec3, Seiteb2) → PunktC2
  70. Angle(R, PunktC2, PunktB2) → μ
  71. Angle(PunktA2, R, PunktC2) → ν
  72. Segment(PunktB2, PunktC2) → Seiteb3
  73. Segment(PunktA, PunktB4) → Seitea4
  74. Circle(PunktB4, 5.5) → c
  75. Point(c) → S
  76. Point(c) → U
  77. CircleArc(PunktB4, U, S) → d
  78. Circle(PunktA, 3) → e
  79. Point(e) → V
  80. Point(e) → W
  81. CircleArc(PunktA, W, V) → g
  82. Intersect(d, g) → PunktD4, , ,
  83. Point(Circle[PunktD4, 3.5]) → PunktC4
  84. Segment(PunktD4, PunktC4) → Seitec4
  85. Segment(PunktA, PunktD4) → Seited4
  86. Segment(PunktB4, PunktC4) → Seiteb4
  87. Angle(PunktB4, PunktA, PunktD4) → ξ
  88. Angle(PunktA, PunktD4, PunktC4) → ο
  89. Angle(PunktC4, PunktB4, PunktA) → ρ
  90. Angle(PunktD4, PunktC4, PunktB4) → σ
  91. Segment(PunktA2 + (0, 0.12), PunktA2 - (0, 0.12)) → seg1
  92. Segment(PunktB2 + (0, 0.12), PunktB2 - (0, 0.12)) → seg2
  93. Intersect(f, Seitea2) → D
  94. Angle(PunktB2, D, P) → τ
  95. Circle(D, 4) → k
  96. Point(k) → Z
  97. Point(k) → A_1
  98. CircleArc(D, Z, A_1) → p
  99. Segment(PunktA + (0, 0.12), PunktA - (0, 0.12)) → seg3
  100. Segment(PunktB4 + (0, 0.12), PunktB4 - (0, 0.12)) → seg4
  101. Segment(PunktD4, PunktD4 + (5, 0)) → i
  102. Circle(PunktD4, 3.5) → q
  103. Point(q) → B_1
  104. Point(q) → C_1
  105. CircleArc(PunktD4, B_1, C_1) → r

AI Drawing Prompt Reference

Construct an isosceles trapezoid in the plane. Start by drawing a circle centered at a base point and taking a point on it, then rotate this point counterclockwise by 40 degrees around the base point to create a new point, connecting the base point with both points to form the first angle. Next, rotate the base point clockwise by 70 degrees around the first point to obtain another new point, and connect these two points to form a second angle. Select points on each ray of the first angle and on one ray of the second angle. Draw an arc centered at the point on the first angle's ray, and find its intersection with a line through that point parallel to the base segment to determine one vertex of the trapezoid. Use the intersection of this parallel line with the other leg to find the adjacent vertex, then connect all vertices sequentially to complete the isosceles trapezoid.
The prompt above was compiled from the original drawing commands and is for reference only.