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Constructing a Parallelogram

Constructing a Parallelogram
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2023-12-06 20:43
PolygonVectorGeometric Construction
In collections Parallelogramm und Raute: Eigenschaften und Konstruktionen
This example demonstrates how to construct a parallelogram using geometric tools. Key mathematical concepts include parallel lines, angles, and polygons. Using GeoGebra commands such as Join, Polygon, and Vector, students can learn to accurately construct special quadrilaterals. Suitable for 5-6 grade students to practice geometric construction.

GeoGebra Commands & Parameters

  1. Join(Sequence[Shuffle[{1, 2, 3, 4, 5, 6, 7}], i, 1, 20]) → listNumSolution
  2. Flatten(Sequence[Sequence[P + ((c * widthcell) * (1, 0)) + ((r * heightcell) * (0, 1)), c, 0, cells], r, 0, cells]) → gridPoints
  3. Unique(val) → valsingle
  4. Point(gridPoints) → A
  5. Point(gridPoints) → B
  6. Point(gridPoints) → C
  7. Point(gridPoints) → D
  8. Polygon(A, B, C, D) → vieleck1, a, b, c, d
  9. Angle(Polygon[A, B, C, D]) → α, β, γ, δ
  10. CountIf(M ≟ Join[aktuell], M, val) → countSame
  11. Textfield(input1) → InputBox1
  12. Textfield(input2) → InputBox2
  13. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  14. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {9, 4, 10, 10, 3, 6, 6, 4, 0, 4, 0, 7, 0, 7, 2, 5, 9, 8, 2, 8, 1, 5, 4, 2, 10, 4, 7, 8, 2, 2, 10, 6, 5, 5, 2, 6, 1, 0, 9, 5, 9, 6, 0, 5, 4, 5, 4, 5, 1, 9, 9, 10, 1, 3, 6, 0, 4, 2, 4, 0, 0, 2, 10, 6, 7, 2, 1, 8, 4, 1, 10, 7, 9, 10, 9, 9, 0, 3, 4, 7, 1, 6, 0, 1, 6, 8, 8, 8, 3, 2, 5, 3, 3, 3, 10, 0, 10, 8, 6, 1}
  15. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  16. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {5, 8, 1, 4, 6, 8, 2, 7, 8, 7, 7, 10, 9, 3, 8, 6, 5, 0, 6, 3, 8, 10, 0, 4, 10, 6, 3, 8, 10, 0, 6, 6, 5, 4, 5, 2, 3, 4, 1, 1, 1, 9, 5, 5, 4, 4, 1, 10, 10, 8, 0, 0, 5, 7, 6, 6, 3, 9, 4, 9, 1, 1, 6, 10, 6, 0, 5, 8, 10, 0, 7, 3, 7, 2, 5, 6, 8, 5, 1, 7, 0, 9, 1, 5, 5, 10, 10, 5, 10, 2, 7, 9, 0, 6, 0, 1, 9, 5, 9, 4}
  17. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  18. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  19. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  20. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  21. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  22. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  23. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  24. Element(gridPoints, g) → PunktVersuch
  25. Vector(A, B) → v1
  26. Vector(A, D) → v2
  27. Angle(v1, v2) → alpha
  28. LaTeX(isSquare, true, true) → Text1
  29. LaTeX(isRectangle, true, true) → Text2
  30. LaTeX(isParallel, true, true) → Text3
  31. Length(val) → lengthval
  32. If(Defined[valsingle], Length[valsingle], 0) → lengthvalsingle
  33. LaTeX(isRhombus, true, true) → Text11
  34. LaTeX(sameInput, true, true) → Text12
  35. Polygon(listSolutionPoints) → vieleckSolution

AI Drawing Prompt Reference

Draw a parallelogram to demonstrate its construction. First, mark four vertices on a grid using the point tool, then connect these points to form the parallelogram. Next, label the opposite sides and interior angles of the parallelogram, and calculate the lengths of the diagonals. Finally, use vector tools to represent the side vectors of the parallelogram and verify that opposite sides are parallel.
The prompt above was compiled from the original drawing commands and is for reference only.