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Pentagon with Rotational Symmetry

Pentagon with Rotational Symmetry
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2018-05-07 09:56
PolygonTrigonometry
This example demonstrates the rotational symmetry of a pentagon. Key mathematical concepts include rotation symmetry and geometric construction. Using GeoGebra commands such as Line, Circle, and Rotate, a pentagon with rotational symmetry can be constructed. Suitable for middle school and above students to learn about geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Circle(A, B) → c
  3. OrthogonalLine(A, f) → g
  4. Intersect(c, f, 2) → C
  5. Segment(A, C) → h
  6. Midpoint(h) → D
  7. Circle(D, C) → d
  8. Intersect(c, g, 1) → E
  9. Ray(E, D) → i
  10. Intersect(d, i, 2) → F
  11. Intersect(d, i, 1) → G
  12. Circle(E, G) → e
  13. Circle(E, F) → k
  14. Intersect(c, g, 2) → H
  15. Intersect(c, e, 2) → I
  16. Intersect(c, e, 1) → J
  17. Polygon(I, J, 5) → poly1, j, l, m, n, p, K, L, M
  18. Point(c) → N
  19. Segment(N, A) → q
  20. Rotate(N, (-(72°)), A) → N'
  21. Angle(N', A, N) → α
  22. Polygon(N', N, 5) → poly2, r, s, t, a, b, O, P, Q
  23. Angle(P, A, H) → β