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Draw Similar Parallelograms

Draw Similar Parallelograms
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2018-03-03 01:08
PolygonTransformationGeometric Construction
This example demonstrates how to construct similar parallelograms. It involves core mathematical concepts such as properties of parallelograms, similarity criteria for shapes, and geometric transformations. GeoGebra commands and objects like Join, Point, Sort, Polygon, If, Circle, Ray, Rotate, Angle, Segment, Line, LaTeX, Random are used in the construction. Suitable for high school students to learn and understand the construction methods of similar shapes and applications of geometric transformations.

GeoGebra Commands & Parameters

  1. Join({Sequence[Sequence[(i, j), i, -10, 10, 1], j, -10, 10, 1], {(15, 6.5), (16.5, 6.5), (18, 6.5), (19.5, 6.5)}}) → GridSpace
  2. Point(GridSpace) → A1
  3. Point(GridSpace) → B1
  4. Point(GridSpace) → C1
  5. Point(GridSpace) → D1
  6. Sort({A1, B1, C1, D1}) → ListX
  7. Polygon((10.5, 9), (25, 9), (25, -10), (10.5, -10)) → RightBox, j, k, l, m
  8. Polygon((14, 7.2), (14, 5.8), (20.5, 5.8), (20.5, 7.2)) → PointsBox, n, p, q, r
  9. Polygon((-12, 7.4), (25, 7.4), (25, 15), (-12, 15)) → TopBox, f, g, h, i
  10. If(y(Element[ListX, 1]) ≥ y(Element[ListX, 2]) ∧ y(Element[ListX, 3]) ≥ y(Element[ListX, 4]) ∨ y(Element[ListX, 1]) ≤ y(Element[ListX, 2]) ∧ y(Element[ListX, 3]) ≤ y(Element[ListX, 4]), Polygon[Element[ListX, 2], Element[ListX, 1], Element[ListX, 3], Element[ListX, 4]], Polygon[Element[ListX, 1], Element[ListX, 2], Element[ListX, 3], Element[ListX, 4]]) → ABC1
  11. Polygon(Acorr, Bcorr, Ccorr, Dcorr) → ABCcorr, i_1, j_1, k_1, l_1
  12. Circle((0, 0), 7) → Circ1
  13. Point(Circ1) → RotPt
  14. Ray(C, RotPt) → s
  15. Rotate(RotPt, (angledisp * π / 180)) → RotPtb
  16. Ray(C, RotPtb) → t
  17. Angle(RotPtb, C, RotPt) → HelpAngle
  18. Segment((0, 7.3), (0, -8)) → yaxis
  19. Polygon(A, B, C, D) → q1, a, b, c, d
  20. Line(A, C) → DiagL1
  21. Line(D, B) → DiagL2
  22. LaTeX("\textbf{Instructions\text{:}}\ Drag\ the\ points\ onto\ the\ grid\ to\ draw\ the\ similar\ quadrilateral.") → Instructions2
  23. Random(0, 1) → UDShiftDirection
  24. Random(0, 1) → LRShiftDirection
  25. LaTeX("Draw\ a\ quadrilateral\ that\ is\ similar\ to\ ABCD\ by\ a\ scale\ factor\ of\ " + ScaleDisplay + ".") → Instructions1
  26. If(ScaleIndex ≟ 1 ∨ ScaleIndex ≟ 2 ∨ ScaleIndex ≟ 3, LaTeX["of\ the\ distance\ from\\ O\ to\ A,\,B,\,C,\, and\ D."], LaTeX["times\ as\ far\ from\\ O\ as\ A,\,B,\,C,\, and\ D."]) → ScaleWording
  27. LaTeX("The\ quadrilateral\ you\\ have\ drawn\ is\ similar\ to\\ ABCD\ but\ not\ by\ a\\ scale\ factor\ of\ " + ScaleDisplay + ".\\ Use\ the\ grid\ to\ place\ the\\ points\ " + ScaleDisplay + "\ " + ((ScaleWording * "."))) → FBSimilar
  28. Sort({A, B, C, D}) → SortedQuadList

AI Drawing Prompt Reference

Draw a parallelogram on a grid and create a similar one using rotation and translation. First, select four points on the grid to form a parallelogram, then rotate this parallelogram around one of its vertices by a certain angle to get a new parallelogram. Ensure the two parallelograms are similar and display the relationships between their corresponding sides and angles.
The prompt above was compiled from the original drawing commands and is for reference only.