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Shapes with the Same Perimeter

Shapes with the Same Perimeter
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2018-01-23 23:05
PolygonTransformationGeometric Construction
This example demonstrates different shapes with the same perimeter. It involves core concepts of similarity transformation and geometric construction. Using GeoGebra commands such as Line, Intersect, Point, Join, etc., it constructs quadrilaterals with the same perimeter. Suitable for middle school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → h
  2. Line(D, h) → i
  3. Line(A, D) → f
  4. Line(B, f) → g
  5. Intersect(i, g) → C
  6. Point(GridSpaceQ) → Q
  7. Join(Sequence[Sequence[(i, j), i, 34, 74, 1], j, 12, 32, 1]) → GridSpace
  8. Point(GridSpace) → P
  9. Line(P, Q) → j
  10. Point(GridSpace) → S
  11. Line(S, j) → k
  12. Line(P, S) → l
  13. Line(Q, l) → m
  14. Intersect(m, k) → R
  15. Segment(S, R) → RS
  16. Segment(C, D) → CD
  17. Segment(A, B) → AB
  18. Segment(B, C) → BC
  19. Segment(D, A) → DA
  20. Segment(Q, P) → PQ
  21. Segment(R, Q) → QR
  22. Segment(P, S) → SP
  23. Point(GridSpace) → P2
  24. Point(GridSpace) → Q2
  25. Segment(A2, B2) → AB2
  26. Segment(B2, C2) → BC2
  27. Segment(C2, A2) → CA2
  28. Segment(P2, Q2) → PQ2
  29. Point(GridSpaceR) → R2
  30. Segment(Q2, R2) → QR2
  31. Segment(R2, P2) → RP2
  32. Intersect(OrthogonalLine[A2, Line[B2, C2]], Line[B2, C2]) → H2Tri
  33. Segment(H2Tri, H1Tri) → HeightDisp1Tri
  34. Intersect(OrthogonalLine[P2, Line[Q2, R2]], Line[Q2, R2]) → H4Tri
  35. Segment(H4Tri, H3Tri) → HeightDisp2Tri
  36. Intersect(OrthogonalLine[B, Line[C, D]], Line[C, D]) → H2Quad
  37. Intersect(OrthogonalLine[Q, Line[R, S]], Line[R, S]) → H4Quad
  38. Segment(H2Quad, H1Quad) → HeightDisp1Quad
  39. Segment(H4Quad, H3Quad) → HeightDisp2Quad
  40. Segment(H4Tri, Q2) → HeightDispHoriz2Tri
  41. Segment(H2Tri, B2) → HeightDispHoriz1Tri
  42. Segment(H4Quad, S) → HeightDispHoriz2Quad
  43. Segment(H2Quad, C) → HeightDispHoriz1Quad
  44. Angle(A2, H2Tri, C2) → Ang1Tri
  45. Angle(P2, H4Tri, R2) → Ang2Tri
  46. Angle(B, H2Quad, C) → Ang1Quad
  47. Angle(Q, H4Quad, R) → Ang2Quad
  48. Rotate(A2, 2, B2) → A2'
  49. Angle(C2, B2, A2) → AngABCRtTri
  50. Angle(A, B, C) → AngABCRtQuad
  51. Angle(A2, C2, B2) → AngACBRtTri
  52. Angle(R2, Q2, P2) → AngPQRRtTri
  53. Angle(Q2, R2, P2) → AngPRQRtTri
  54. Angle(P, Q, R) → AngPQRRtQuad