MathPlotAI Logo MathPlotAI

Parallelogram Construction and Geometric Drawing

Parallelogram Construction and Geometric Drawing
Loading the math board and drawing, please wait…
2023-12-06 20:40
PolygonAngleGeometric Construction
In collections Parallelogramm und Raute: Eigenschaften und Konstruktionen
This example demonstrates how to construct a parallelogram using GeoGebra tools, involving concepts such as geometric construction, angle measurement, and segment length calculation. The construction steps include using tools like Geodreieck, Zirkel, and Lineal, along with GeoGebra commands such as Point, Segment, Angle, and Intersect. It is suitable for elementary and middle school students learning geometry, both for classroom use and independent practice.

GeoGebra Commands & Parameters

  1. Point(Line[Vick1, xAxis]) → Car1
  2. Sequence(true, m, 1, maxstep) → listfixed
  3. Textfield(input1) → Eingabefeld1
  4. Textfield(input2) → Eingabefeld2
  5. Point(Line[I1, xAxis]) → J1
  6. If(step ≟ 5, Car1 + (0, -1), step ∈ {1, 5}, Car1, Car2) → PCar
  7. Point(Line[H1, xAxis]) → H2
  8. Point(Line[PCar, xAxis]) → H
  9. Point(Line[E, xAxis]) → F
  10. Segment(A1, B1) → aa1
  11. Segment(A1, D10) → ba2k
  12. Angle(B1, A1, D10) → aalpha
  13. Segment(D1, C10) → aa2k
  14. SpeechBubbleRight(S1, 12.25, 1.05) → Vieleck1
  15. Segment(B1, B1 + ((scale1 * 6.5) * UnitVector[Vector[A1, D1]])) → ba1k
  16. Angle(C1, B1, A1) → abeta
  17. Angle(D1, C1, B1) → agamma
  18. Angle(A1, D1, C1) → adelta
  19. If(a ≟ 2, J1, J2) → J
  20. If(a ≟ 2, I1, I2) → I
  21. If(step ≟ 3, (11, -7.38), (11.28726, -7.38894)) → M2
  22. Segment(A2, B2) → ab1
  23. Intersect(Circle[A2, (6 * scale2)], Segment[B2, C20]) → C2,
  24. Segment(A2, C2) → eb
  25. CircleArc(A2, Rotate[C2, (360 - 6)°, A2], Rotate[C2, 6°, A2]) → d
  26. Segment(B2, C2) → bb1
  27. Segment(C2, C20) → bb1k
  28. Segment(D2, D2 + Vector[C2, C20]) → bb2k
  29. Segment(A2, D2) → bb2
  30. Segment(D2, D2 + ((0.6 * scale2) * Vector[(0, 0), (-1, 0)])) → ab2k
  31. Segment(D2, C2) → ab2
  32. Segment(D2, B2) → fb
  33. Angle(Polygon[A2, B2, C2, D2]) → balpha, bbeta, bgamma, bdelta
  34. If(step ≟ 3 ∧ b ≟ 2 ∨ step ≟ 4 ∧ c ≟ 2, N1, N2) → N
  35. If(step ≟ 3 ∧ b ≟ 2 ∨ step ≟ 4 ∧ c ≟ 2, M1, M2) → M
  36. Segment(A3, B3) → ac1
  37. CircleArc(A1, Rotate[D1, (360 - 10)°, A1], Rotate[D1, 10°, A1]) → e
  38. Intersect(Circle[A3, (scale3 * 5)], Circle[B3, (scale3 * 11)]) → D3, D30, ,
  39. CircleArc(A3, Rotate[D3, (360 - 12)°, A3], Rotate[D3, 12°, A3]) → c_1
  40. CircleArc(B3, Rotate[D3, (360 - 10)°, B3], Rotate[D3, 10°, B3]) → d_1
  41. Segment(A3, D3) → bc2
  42. Segment(B3, D3) → fc
  43. Segment(B3, C3) → bc1
  44. Segment(C3, C3 + UnitVector[Vector[B3, C3]]) → bc1k
  45. Segment(D3, C3) → ac2
  46. Segment(A3, C3) → ec
  47. Angle(Polygon[A3, B3, C3, D3]) → calpha, cbeta, cgamma, cdelta
  48. Segment(C3, C3 + ((scale3 * 2.5) * UnitVector[Vector[D3, C3]])) → ac2k
  49. Point(Line[Vick1, xAxis]) → Max1
  50. If(step ≟ 5, Vick1 + (0, -1), step ∈ {1, 5}, Vick1, Vick2) → PVick
  51. If(step ≟ 5, Max1 + (0, -1), step ∈ {1, 5}, Max1, Max2) → PMax
  52. Element({1, 2, 3} \ {chosen1, chosen2}, 1) → chosen3
  53. Segment(A1, D1) → ba2
  54. Segment(B1, C1) → ba1
  55. Segment(A1, C1) → ea

AI Drawing Prompt Reference

On a coordinate plane, set up construction points to form a quadrilateral: place two points A and B as the base endpoints, and choose points D and C to complete the vertex set. Draw the key segments connecting A to B, A to D, D to C, and the remaining sides so that A–B–C–D forms a closed polygon. At each vertex, mark the interior angles defined by the three surrounding points. Use the drawn segments and angle measurements to emphasize the parallelogram-like geometric relationships, extending segments along the intended directions when constructing C and D so opposite sides align.
The prompt above was compiled from the original drawing commands and is for reference only.