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Similarity Transformation Exercise 2

Similarity Transformation Exercise 2
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2016-03-24 14:24
PolygonTransformationGeometric Construction
In collections Dilation and Similarity Project: Part One Obstar Dilation and Similarity Exploration
This example demonstrates the properties of similarity transformations in polygons, including dilation, rotation, and reflection. It involves core mathematical concepts such as similarity, geometric transformations, vectors, and coordinate geometry. The construction uses commands like Polygon, Angle, Segment, Dilate, Rotate, Mirror, Vector, and Line in GeoGebra. Suitable for high school students to learn geometric transformations and polygon properties, as well as for mathematical demonstrations and teaching purposes.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Polygon(E, F, G, H) → poly2, e, f, g, h
  3. Angle(B, A, D) → α
  4. Angle(A, D, C) → β
  5. Angle(D, C, B) → γ
  6. Angle(C, B, A) → δ
  7. Polygon(M, N, O, P, Q, R, S, T) → poly3, m, n, o, p, q, r, s, t
  8. Segment(U, V) → l
  9. Dilate(M, 2.5, W) → M'
  10. Dilate(N, 2.5, W) → N'
  11. Dilate(O, 2.5, W) → O'
  12. Dilate(P, 2.5, W) → P'
  13. Dilate(Q, 2.5, W) → Q'
  14. Dilate(R, 2.5, W) → R'
  15. Dilate(S, 2.5, W) → S'
  16. Dilate(T, 2.5, W) → T'
  17. Rotate(M', 90) → M''
  18. Rotate(N', 90) → N''
  19. Rotate(O', 90) → O''
  20. Rotate(P', 90) → P''
  21. Rotate(Q', 90) → Q''
  22. Rotate(R', 90) → R''
  23. Rotate(S', 90) → S''
  24. Rotate(T', 90) → T''
  25. Polygon(M'', N'', O'', P'', Q'', R'', S'', T'') → poly4, m'', n'', o'', p'', q'', r'', s'', t''
  26. Segment(Z, A_1) → a_1
  27. Mirror(M', a_1) → M''_1
  28. Mirror(N', a_1) → N''_1
  29. Mirror(O', a_1) → O''_1
  30. Mirror(P', a_1) → P''_1
  31. Mirror(Q', a_1) → Q''_1
  32. Mirror(R', a_1) → R''_1
  33. Mirror(S', a_1) → S''_1
  34. Mirror(T', a_1) → T''_1
  35. Polygon(M''_1, N''_1, O''_1, P''_1, Q''_1, R''_1, S''_1, T''_1) → poly3'', m''_1, n''_1, o''_1, p''_1, q''_1, r''_1, s''_1, t''_1
  36. Angle(T''_1, M''_1, N''_1) → ι
  37. Angle(M''_1, N''_1, O''_1) → κ
  38. Angle(N''_1, O''_1, P''_1) → λ
  39. Angle(O''_1, P''_1, Q''_1) → μ
  40. Angle(P''_1, Q''_1, R''_1) → ν
  41. Angle(Q''_1, R''_1, S''_1) → ξ
  42. Angle(R''_1, S''_1, T''_1) → ο
  43. Angle(S''_1, T''_1, M''_1) → ρ
  44. Angle(O, N, M) → σ
  45. Angle(N, M, T) → τ
  46. Angle(M, T, S) → υ
  47. Angle(T, S, R) → ϕ
  48. Angle(S, R, Q) → χ
  49. Angle(R, Q, P) → ψ
  50. Angle(Q, P, O) → ω
  51. Angle(P, O, N) → α_1
  52. Rotate(E, 45°, B_1) → E'
  53. Rotate(F, 45°, B_1) → F'
  54. Rotate(G, 45°, B_1) → G'
  55. Rotate(H, 45°, B_1) → H'
  56. Polygon(E', F', G', H') → poly2', e', f', g', h'
  57. Vector(D_1, E_1) → u
  58. Vector(F_1, G_1) → v
  59. Angle(E', F', G') → ε
  60. Angle(F', G', H') → ζ
  61. Angle(G', H', E') → η
  62. Angle(H', E', F') → θ
  63. Line(S''_1, S) → i
  64. Line(T''_1, T) → j
  65. Line(P''_1, P) → k

AI Drawing Prompt Reference

Draw a quadrilateral ABCD and an octagon MNOPTQRS, then dilate the octagon by 2.5 times, rotate it 90 degrees, mirror it across line segment ZA1, and finally measure the angles of the dilated, rotated, and mirrored octagon.
The prompt above was compiled from the original drawing commands and is for reference only.