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Geometric Construction of a Deltoid (Kite)

Geometric Construction of a Deltoid (Kite)
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2023-06-16 16:09
PolygonAngleGeometric Construction
In collections Deltoid - Eigenschaften und Konstruktionen
This example demonstrates how to construct a deltoid (kite) using GeoGebra. The core mathematical concepts include the definition and properties of a deltoid (four equal sides, diagonals perpendicular and bisect each other). Construction uses Polygon command for drawing, Angle for measuring angles to verify properties, Segment for edges, Stretch for transformations, combined with If conditions and Textfield for interactive exercises. Suitable for Grade 5-6 students to master geometric construction tools (compass, ruler, protractor or DGS) and develop skills in constructing special quadrilaterals.

GeoGebra Commands & Parameters

  1. Join(Sequence[Join[{Shuffle[Sequence[1, 7]], Shuffle[Sequence[8, 14]]}], m, 1, 9]) → listExNums
  2. If(Mod[exnum, 7] ≟ 0, 7, Mod[exnum, 7]) → typ
  3. Element({10, 10, 9, 9, 8, 8, 12}, typ) → maxstep
  4. Element({M1, M2, M3, M4, M5, M6, M7, M8, M9, M10, M11, M12, M13, M14}, exnum) → M
  5. Textfield(input1) → InputBox1
  6. Textfield(input2) → InputBox2
  7. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  8. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {7, 5, 7, 7, 4, 0, 2, 5, 9, 8, 0, 9, 4, 7, 5, 2, 7, 10, 5, 0, 2, 10, 1, 3, 2, 8, 10, 4, 1, 7, 6, 6, 3, 5, 1, 6, 10, 9, 3, 5, 2, 1, 5, 1, 7, 8, 7, 2, 2, 10, 5, 9, 7, 5, 5, 6, 10, 8, 0, 3, 2, 9, 5, 0, 2, 7, 2, 0, 1, 8, 5, 3, 6, 0, 5, 4, 4, 9, 6, 1, 10, 4, 5, 8, 5, 1, 5, 0, 8, 0, 1, 3, 2, 2, 7, 4, 6, 0, 1, 1}
  9. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  10. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {4, 9, 6, 6, 2, 3, 4, 1, 7, 5, 7, 10, 2, 7, 4, 1, 4, 2, 9, 8, 5, 9, 5, 6, 0, 10, 3, 6, 2, 5, 5, 8, 2, 5, 8, 1, 1, 2, 7, 6, 6, 10, 10, 9, 4, 5, 2, 2, 3, 6, 4, 7, 5, 7, 5, 6, 2, 6, 10, 6, 5, 5, 7, 4, 9, 8, 4, 7, 1, 2, 7, 0, 10, 1, 0, 4, 10, 5, 5, 10, 6, 10, 5, 8, 6, 5, 8, 5, 2, 1, 8, 3, 1, 1, 2, 3, 6, 9, 0, 9}
  11. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  12. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  13. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  14. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  15. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  16. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  17. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  18. Defined((input1 * input2)) → fixed
  19. Angle(B, A, D) → walpha
  20. Angle(C, B, A) → wbeta
  21. LaTeX(typ, true, true) → Text3
  22. Segment(A, B) → a1
  23. Segment(A, D) → a2
  24. Segment(B, C) → b1
  25. Segment(C, D) → b2
  26. Segment(A, M) → eo
  27. Segment(M, C) → eu
  28. Segment(B, D) → f
  29. Zip(If[m < 5, " cm", "°"], m, numValues) → listEH
  30. Angle(A, D, C) → wdelta
  31. Angle(D, C, B) → wgamma
  32. Stretch(A, Line[B, D], 1.2) → A'
  33. Stretch(C, Line[B, D], 1.2) → C'
  34. Segment(A', C') → elang
  35. Stretch(B, Line[A, C], 1.3) → B'
  36. Stretch(D, Line[A, C], 1.3) → D'
  37. Segment(B', D') → flang
  38. Angle(A, M, B) → rechterwinkel
  39. Stretch(B, OrthogonalLine[Midpoint[B, C], Line[B, C]], 1.2) → B'_{1}
  40. Stretch(C, OrthogonalLine[Midpoint[B, C], Line[B, C]], 1.2) → C'_{1}
  41. Segment(B'_{1}, C'_{1}) → b1lang
  42. Stretch(C, OrthogonalLine[Midpoint[C, D], Line[C, D]], 1.2) → C'_{2}
  43. Stretch(D, OrthogonalLine[Midpoint[C, D], Line[C, D]], 1.2) → D'_{1}
  44. Segment(C'_{2}, D'_{1}) → b2lang
  45. Stretch(A, OrthogonalLine[Midpoint[A, D], Line[A, D]], 1.2) → A'_{1}
  46. Stretch(D, OrthogonalLine[Midpoint[A, D], Line[A, D]], 1.2) → D'_{2}
  47. Segment(A'_{1}, D'_{2}) → a2lang
  48. Stretch(A, OrthogonalLine[Midpoint[A, B], Line[A, B]], 1.2) → A'_{2}
  49. Stretch(B, OrthogonalLine[Midpoint[A, B], Line[A, B]], 1.2) → B'_{2}
  50. Segment(A'_{2}, B'_{2}) → a1lang
  51. Element({2, 1, 3, 3, 4, 3, 4}, typ) → numCheckValue
  52. If((checkValue * 10) - floor((checkValue * 10)) ≥ 0.5, (floor((checkValue * 10)) * 0.1) + 0.1, (floor((checkValue * 10)) * 0.1)) → checkValueGerundet
  53. If(step ≟ 1, G_1, G_2) → G
  54. If(step ≟ 1, H_1, H_2) → H
  55. Angle(B, M, C) → rechterwinkel2

AI Drawing Prompt Reference

Draw a kite shape with four equal sides and diagonals that are perpendicular and bisect each other. Start by creating a quadrilateral with equal side lengths, then measure the angles at the intersection of the diagonals to confirm they are right angles. Next, stretch one pair of diagonals outward while maintaining the equal side lengths, observing how the shape changes. Finally, draw the diagonals inside the quadrilateral, label their intersection point and key angles, to highlight the kite's geometric properties.
The prompt above was compiled from the original drawing commands and is for reference only.