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Convex or Concave Polygons

Convex or Concave Polygons
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2020-01-20 16:43
PolygonAngleGeometric Construction
This example demonstrates how to distinguish between convex and concave polygons by adjusting the vertices. Key mathematical concepts include properties of polygons, angle measurement, and geometric construction. Using GeoGebra commands such as Segment, Line, Angle, and Polygon, the shape of the polygon can be dynamically changed to observe changes in its convexity or concavity. Suitable for middle school and above students and teachers.

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, Length[Liste1]], j, 2, 5) → liste2
  29. Join(liste2) → liste1
  30. RemoveUndefined(liste1) → liste3
  31. If(Length[liste3] ≥ 1, 1, 0) → mm
  32. If(o ∧ z ≤ 0.1, "Convex polygon", If[(¬o) ∧ z ≤ 0.1, "Non-convex or concave polygon"]) → texte3