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Symmetry Beauty of Polygons

Symmetry Beauty of Polygons
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2019-04-14 08:55
PolygonCoordinate GeometryTransformation
This example demonstrates the symmetry beauty of polygons. It involves key mathematical concepts such as polygons, geometric transformations, and coordinate geometry. Using GeoGebra commands like Polygon, LineBisector, Intersect, Circle, Point, and Segment, you can construct symmetric polygons. Suitable for middle school and above students or teachers for geometric construction and symmetry teaching.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 5) → poly1, f, g, h, i, j, C, D, E
  2. LineBisector(E, A) → k
  3. LineBisector(E, D) → l
  4. Intersect(k, l) → F
  5. Circle(F, 13) → d
  6. Point(d) → L
  7. Segment(L, D) → q
  8. Segment(L, E) → r
  9. Segment(L, A) → s
  10. Segment(L, B) → a
  11. Segment(L, C) → t
  12. LineBisector(C, D) → p
  13. Intersect(p, h) → I
  14. Circle(F, C) → e
  15. Point(e) → M
  16. Segment(F, M) → f_1
  17. Intersect(l, i) → G
  18. Intersect(k, j) → H
  19. LineBisector(A, B) → m
  20. LineBisector(B, C) → n
  21. Intersect(n, g) → J
  22. Intersect(m, f) → K

AI Drawing Prompt Reference

Draw a pentagon ABCDE, find its symmetry center F, draw a circle with F as the center, then pick a point L on the circle and connect L to each vertex of the pentagon. Next, find the intersection points of the symmetry axes and connect these points to form a new symmetric figure.
The prompt above was compiled from the original drawing commands and is for reference only.