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Draw Similar Rectangles

Draw Similar Rectangles
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2018-03-02 22:24
PolygonCoordinate GeometryGeometric Construction
This example demonstrates how to draw similar rectangles using GeoGebra. It involves core mathematical concepts like rectangles, similar figures, ratios, and special points. Key GeoGebra commands and objects used include Join, Point, Sort, Polygon, If, Circle, Ray, Rotate, Angle, Segment, Random, LaTeX, Line. Suitable for middle school and above students to explore properties of similar figures.

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. Random(2, 4) → ScaleFactor
  20. LaTeX("Draw\ a\ rectangle\ that\ is\ similar\ to\ ABCD\ by\ a\ scale\ factor\ of\ " + ScaleFactor + "\ using\ the\ method\ described\\ in\ the\ previous\ example.") → Instructions1
  21. Random(1, 3) → HorizontalLength
  22. Random(1, 2) → VerticalLength
  23. Polygon(A, B, C, D) → q1, a, b, c, d
  24. Line(A, C) → DiagL1
  25. Line(D, B) → DiagL2
  26. LaTeX("\textbf{Instructions\text{:}}\ Drag\ the\ points\ onto\ the\ grid\ to\ draw\ the\ similar\ quadrilateral.") → Instructions2
  27. LaTeX("The\ quadrilateral\ you\\ have\ drawn\ is\ similar\ to\\ ABCD\ but\ not\ by\ a\\ scale\ factor\ of\ " + ScaleFactor + ".\\ Use\ the\ grid\ to\ place\ the\\ points\ " + ScaleFactor + "\ times\ as\ far\ from\\ O\ as\ A\ B\ C,\, and\ D.") → FBSimilar
  28. Sort({A, B, C, D}) → SortedQuadList