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Regular Polygon - Reflection Symmetry

Regular Polygon - Reflection Symmetry
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2016-07-12 00:27
PolygonTransformation
This example demonstrates the reflection symmetry of a regular polygon. It involves key mathematical concepts such as reflection and geometric construction. Using GeoGebra commands like Polygon, Segment, Vector, Translate, LineBisector, and Intersect, one can construct a regular polygon and observe its reflection symmetry. Suitable for middle school and above students to learn about geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. Segment(A, C) → i
  3. Segment(C, B) → j
  4. Segment(B, A) → k
  5. Vector(D, E) → u
  6. Vector(F, G) → v
  7. Translate(A, u) → A'
  8. Translate(C, u) → C'
  9. Segment(A', C') → i'
  10. Translate(C, u) → C'_1
  11. Translate(B, u) → B'
  12. Segment(C'_1, B') → j'
  13. Translate(B, u) → B'_1
  14. Translate(A, u) → A'_1
  15. Segment(B'_1, A'_1) → k'
  16. Translate(A, v) → A'_2
  17. Translate(C, v) → C'_2
  18. Segment(A'_2, C'_2) → i'_1
  19. Translate(C, v) → C'_3
  20. Translate(B, v) → B'_2
  21. Segment(C'_3, B'_2) → j'_1
  22. Translate(B, v) → B'_3
  23. Translate(A, v) → A'_3
  24. Segment(B'_3, A'_3) → k'_1
  25. LineBisector(A, B) → l
  26. LineBisector(A', C') → m
  27. LineBisector(C'_2, B'_2) → n
  28. Intersect(l, k) → H
  29. Polygon(A, H, C) → poly2, c, a, h_1
  30. Intersect(m, i') → I
  31. Polygon(C', I, B') → poly3, b', c', i_1
  32. Intersect(n, j'_1) → J
  33. Polygon(A'_2, C'_2, J) → poly4, j_1, a'_2, c'_2