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Convex, Concave and Crossed Polygons

Convex, Concave and Crossed Polygons
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2013-03-28 10:07
PolygonGeometric ConstructionSlider Animation
Move points to change the shape of the polygon and demonstrate the differences between convex, concave, and crossed polygons. Key mathematical concepts include the definition and classification of polygons. GeoGebra commands such as Segment, Line, Distance, Angle, and Polygon are used to construct the polygon. Suitable for students at the middle school level and above to learn about the properties and classification of polygons.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Line(A, B) → h
  3. Segment(B, C) → b
  4. Segment(C, D) → c
  5. Line(C, D) → j
  6. Segment(D, E) → d
  7. Line(D, E) → k
  8. Segment(E, F) → e
  9. Line(E, F) → l
  10. Segment(F, G) → f
  11. Line(F, G) → m
  12. Segment(G, H) → g
  13. Line(G, H) → n_2
  14. Line(C, B) → i
  15. Distance(A, H) → z
  16. Segment(A, H) → r_2
  17. Angle(A, B, C) → α
  18. Angle(B, C, D) → β
  19. Angle(C, D, E) → γ
  20. Angle(D, E, F) → δ
  21. Angle(E, F, G) → ε
  22. Angle(F, G, H) → ζ
  23. Angle(G, H, A) → η
  24. Angle(H, A, B) → θ
  25. Angle(G, A, B) → ι
  26. Polygon(A, B, C, D, E, F, G) → poly1, a_1, b_1, c_1, d_1, e_1, f_1, g_1
  27. Intersect(a, c) → I
  28. Sequence(Sequence[Intersect[Element[Liste1, i], Element[Liste1, i + j]], i, 1.0, Length[Liste1]], j, 2.0, 5.0) → liste2
  29. Join(liste2) → liste1
  30. RemoveUndefined(liste1) → liste3
  31. If(Length[liste3] ≥ 1.0, 1.0, 0.0) → mm
  32. If(o ∧ z ≤ 0.1, "polygone convexe", If[(¬o) ∧ z ≤ 0.1, "polygone non convexe"]) → texte3

AI Drawing Prompt Reference

Draw a polygon using points A, B, C, D, E, F, G, and H to define its vertices. Connect these points to form the polygon and move them to change its shape, observing whether it is a convex polygon, concave polygon, or crossed polygon. Pay attention to the changes in angles and distances to understand the difference between convex and concave polygons.
The prompt above was compiled from the original drawing commands and is for reference only.