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Lines of Reflective Symmetry Demo

Lines of Reflective Symmetry Demo
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2016-11-09 14:30
CirclePolygonTransformationGeometric Construction
This example demonstrates how to construct and visualize lines of reflective symmetry for polygons. It involves core mathematical concepts like symmetry axes, reflection, polygon construction, and circumcircle of a circle. The construction uses commands such as Rotate, Polygon, Line, Midpoint, Point, Angle, OrthogonalLine, Distance, and Intersect. Suitable for high school mathematics education to understand geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Rotate(B_1, (360 / n)°, O) → A
  2. Polygon(B_1, A, n) → poly1, a, j, B, D, E, F, G, H, I, J, b, c, d, e, f, g, h, i
  3. Line(E, O) → k
  4. Line(D, O) → l
  5. Line(B, O) → m
  6. Line(A, O) → p
  7. Midpoint(A, B) → L
  8. Midpoint(B, D) → M
  9. Line(O, M) → s
  10. Midpoint(A, B_1) → N
  11. Line(N, O) → t
  12. Midpoint(E, D) → O_1
  13. Line(O_1, O) → a_1
  14. Midpoint(F, E) → R
  15. Line(R, O) → b_1
  16. Point(a) → T
  17. Point(b) → V
  18. Angle(B, A, O) → α
  19. Angle(O, A, B_1) → β
  20. Midpoint(A, B) → P
  21. OrthogonalLine(P, b) → q
  22. Angle(A, P, O) → γ
  23. Distance(P, B) → distancePC
  24. Distance(P, A) → distancePB'
  25. Intersect(a, j) → C
  26. Line(O, C) → r