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Graphical Demonstration of Exterior Angles of Polygons

Graphical Demonstration of Exterior Angles of Polygons
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2017-12-22 21:42
PolygonAngleVectorCoordinate GeometryGeometric Construction
In collections Mathematics Form 2
This example visually demonstrates the properties and calculations of exterior angles in polygons. It involves core mathematical concepts like the polygon exterior angle sum theorem, vector operations, and coordinate geometry. GeoGebra commands and objects used include Append, Sequence, Insert, Polygon, PointIn, SelectedIndex, points, vectors, and polygons. Suitable for high school mathematics education and geometric learning, helping to understand the relationship between exterior and interior angles of polygons.

GeoGebra Commands & Parameters

  1. Append(Sequence[LPoint(p), p, 1, n], A) → SPs
  2. Sequence(Segment[SPs(p), SPs(p + 1)], p, 1, n) → Sisi
  3. Sequence(Circle[LPoint(p), r], p, 1, n) → Bulat1
  4. Sequence(Intersect[Bulat1(p), Sisi(p)], p, 1, n) → SP1
  5. Insert(Angle[SPs(2), SPs(1), SPs(-2)], Sequence[Angle[SPs(p), SPs(p - 1), SPs(p - 2)], p, 3, n + 1], 1) → IntAng
  6. Sequence(Rotate[SP1(p), (-(180° - IntAng(p))), SPs(p)], p, 1, n) → SP2
  7. Sequence(CircleSector[SPs(p), SP2(p), SP1(p)], p, 1, n) → Sektor
  8. Polygon(Take[SPs, 1, n]) → Poligon
  9. PointIn(Poligon) → M
  10. Sequence(Vector[SPs(p), M], p, 1, n) → Vektor
  11. Sequence(Translate[Sektor(p), (a * Vektor(p))], p, 1, n) → Mv
  12. Sequence(Line[SPs(p), SP2(p)], p, 1, n) → SLine
  13. Sequence(Circle[LPoint(p), (2 * r)], p, 1, n) → Bulat2
  14. Sequence(Intersect[Bulat2(p), SLine(p), SP2(p)], p, 1, n) → SP3
  15. Sequence(Segment[SPs(p), SP3(p)], p, 1, n) → SSeg
  16. SelectedIndex(Bahasa) → nn