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Perimeter and Area in Similar Polygons

Perimeter and Area in Similar Polygons
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2015-04-14 08:09
PolygonGeometric Construction
This example demonstrates the relationship between the perimeter and area of similar polygons. Key math concepts include similar polygons, perimeter, area, geometric mean, and quadratic equations. It is constructed using GeoGebra commands like Segment, Polygon, Line, Point, Intersect, Angle, PointIn, and Perimeter. Suitable for high school mathematics education to understand the proportional properties of similar polygons.

GeoGebra Commands & Parameters

  1. Segment(A, C) → a
  2. Segment(C, B) → b
  3. Segment(B, A) → c
  4. Polygon(A, C, B) → ABC, b_1, a_1, c_1
  5. Line(A, D) → d
  6. Line(C, D) → e
  7. Line(B, D) → f
  8. Point(d) → E
  9. Line(E, c) → g
  10. Line(E, a) → h
  11. Intersect(e, h) → F
  12. Line(F, b) → i
  13. Intersect(f, g) → G
  14. Segment(G, E) → j
  15. Segment(E, F) → k
  16. Segment(F, G) → l
  17. Polygon(G, E, F) → EGF, f_1, g_1, e_1
  18. Angle(B, A, C) → α
  19. Angle(A, C, B) → β
  20. Angle(A, B, C) → γ
  21. Angle(G, E, F) → δ
  22. Angle(E, F, G) → ε
  23. Angle(F, G, E) → ζ
  24. PointIn(ABC) → Pointpoly1_1
  25. PointIn(EGF) → Pointpoly2_1
  26. PointIn(EGF) → Pointpoly2_2
  27. Segment(H, I) → m
  28. Segment(J, I) → n
  29. Segment(H, K) → q
  30. Segment(J, K) → t
  31. Line(K, L) → d_1
  32. Line(H, L) → h_1
  33. Line(J, L) → i_1
  34. Line(I, L) → j_1
  35. Polygon(H, I, J, K) → poly1, h_2, i_2, j_2, k_1
  36. Point(h_1) → M
  37. Line(M, m) → l_1
  38. Line(M, q) → m_1
  39. Intersect(j_1, l_1) → N
  40. Line(N, n) → n_1
  41. Intersect(i_1, n_1) → O
  42. Line(O, t) → p_1
  43. Intersect(d_1, m_1) → P
  44. Polygon(N, M, P, O) → poly2, n_2, m_2, p_2, o
  45. Angle(N, M, P) → η
  46. Angle(K, H, I) → θ
  47. Angle(P, O, N) → ι
  48. Angle(K, J, I) → κ
  49. Angle(H, K, J) → λ
  50. Angle(H, I, J) → ν
  51. Angle(M, N, O) → ξ
  52. Angle(M, P, O) → ο
  53. PointIn(poly1) → Pointpoly1_2
  54. PointIn(poly2) → Pointpoly2_3
  55. PointIn(poly1) → Pointpoly1_3
  56. Perimeter(ABC) → u
  57. PointIn(poly1) → Pointpoly1
  58. PointIn(poly2) → Pointpoly2
  59. Segment(P, M) → q_1
  60. Segment(M, N) → r_1
  61. Segment(N, O) → s_1
  62. Segment(O, P) → t_1