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Angles in a Regular Polygon

Angles in a Regular Polygon
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2015-07-21 15:03
PolygonAngleGeometric Construction
This example demonstrates the angles between diagonals in a regular polygon. It involves core math concepts like polygons, angle calculations, and geometric constructions. GeoGebra commands/objects used include Intersect, Circle, Sequence, Polygon, Sector, CircleArc, and Angle. Suitable for high school students learning geometry to understand symmetry and angle relationships in regular polygons.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 1) → c
  3. Sequence((cos(((k * 2) * π / n)), sin(((k * 2) * π / n))), k, 1, n) → list1
  4. Polygon(list1) → poly1
  5. Sequence(Segment[P, Element[list1, i]], i, 1, n) → list2
  6. Sector(c, Element[list1, i], Element[list1, i + 1]) → d
  7. CircleArc(O, Element[list1, i], Element[list1, i + 1]) → e
  8. Angle(Element[list1, i], O, Element[list1, i + 1]) → α
  9. Angle(Element[list1, i], P, Element[list1, i + 1]) → β
  10. CircleArc(O, Element[list1, i], Element[list1, i + 1]) → f
  11. Sector(c, Element[list1, 1], Element[list1, 2]) → k
  12. Polygon(P, Element[list1, 1], Element[list1, 2]) → poly3, j, p, l
  13. Polygon(P, Element[list1, i], Element[list1, i + 1]) → poly2, a, p_1, b
  14. Angle(Element[list1, 1], O, Element[list1, 2]) → γ
  15. Angle(Element[list1, 1], P, Element[list1, 2]) → δ
  16. Sequence(Segment[Element[list1, k], O], k, 1, n) → list3
  17. CircleArc(O, Element[list1, 1], Element[list1, 2]) → g
  18. Sequence(Angle[Element[list1, k], P, Element[list1, k + 1]], k, 1, i) → list4