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Similarity in Solid Figures

Similarity in Solid Figures
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2022-09-20 20:51
VectorTrigonometrySolid GeometryTransformationGeometric Construction
This example demonstrates similarity transformations in solid figures like cubes and prisms. It involves core math concepts such as area and volume calculations, along with transformations like dilation and translation. GeoGebra commands used include Dilate, Polygon, Vector, Translate, Intersect, Circle, Point, Line, OrthogonalLine, and Angle. Suitable for high school geometry and transformation learning.

GeoGebra Commands & Parameters

  1. Dilate(E, a, A) → E'_1
  2. Dilate(F, a, D) → F'_1
  3. Dilate(G, a, C) → G'_1
  4. Dilate(A, b, D) → A'_1
  5. Dilate(E'_1, b, F'_1) → E''_1
  6. Dilate(B, b, C) → B'_1
  7. Dilate(F'_1, c, G'_1) → F''_1
  8. Dilate(D, a, B) → D'_1
  9. Dilate(E'_1, c, D'_1) → E''
  10. Dilate(E'', b, F''_1) → E'''
  11. Dilate(A'_1, c, B'_1) → A''_1
  12. Dilate(D, c, C) → D'_2
  13. Polygon(C, G'_1, F''_1, D'_2) → poly1, ur, vr, uc, vc2
  14. Polygon(C, D'_2, A''_1, B'_1) → poly2, vc, wc2, vl, wl
  15. Polygon(A''_1, D'_2, F''_1, E''') → poly3, wc, uc2, wr, ul2
  16. Polygon(B, A, D, C) → poly4, b_1, a_1, d_3, c_3
  17. Polygon(C, D, F, G) → poly5, c_4, d_1, f_2, g_1
  18. Polygon(D, F, E, A) → poly6, d_2, f_1, e_1, a_2
  19. Vector(C, D) → u
  20. Sequence(Segment[Translate[C, Vector[(j * u)]], Translate[G'_1, Vector[(j * u)]]], j, 1, c - 1) → list1
  21. Sequence(Segment[Translate[B'_1, Vector[(j * u)]], Translate[C, Vector[(j * u)]]], j, 1, c - 1) → list2
  22. Vector(C, G) → v
  23. Vector(C, B) → w
  24. Sequence(Segment[Translate[C, Vector[(j * v)]], Translate[D'_2, Vector[(j * v)]]], j, 1, a - 1) → list3
  25. Sequence(Segment[Translate[C, Vector[(j * w)]], Translate[D'_2, Vector[(j * w)]]], j, 1, b - 1) → list4
  26. Sequence(Segment[Translate[F''_1, Vector[(j * w)]], Translate[D'_2, Vector[(j * w)]]], j, 1, b - 1) → list5
  27. Sequence(Segment[Translate[D'_2, Vector[(j * v)]], Translate[A''_1, Vector[(j * v)]]], j, 1, a - 1) → list6
  28. Dilate(G, (a * d), C) → G'
  29. Dilate(F, (a * d), D) → F'
  30. Dilate(F', (c * f), G') → F''
  31. Dilate(D, (c * f), C) → D'
  32. Dilate(B, (b * e), C) → B'
  33. Dilate(A, (b * e), D) → A'
  34. Dilate(A', (c * f), B') → A''
  35. Vector(D', F'') → z
  36. Translate(A'', z) → A'''
  37. Polygon(D', C, G', F'') → poly7, d'_3, ur2, vr2, f_4
  38. Polygon(D', C, B', A'') → poly8, d_6, wl2, vl2, a_4
  39. Polygon(A'', D', F'', A''') → poly9, a''_3, d'_5, wr2, ul
  40. Sequence(Segment[Translate[C, Vector[((j * c) * u)]], Translate[G', Vector[((j * c) * u)]]], j, 1, f) → list7
  41. Sequence(Segment[Translate[C, Vector[((j * c) * u)]], Translate[B', Vector[((j * c) * u)]]], j, 1, f) → list8
  42. Sequence(Segment[Translate[D', Vector[((j * a) * v)]], Translate[C, Vector[((j * a) * v)]]], j, 1, d) → list9
  43. Sequence(Segment[Translate[D', Vector[((j * b) * w)]], Translate[C, Vector[((j * b) * w)]]], j, 1, e) → list10
  44. Sequence(Segment[Translate[A'', Vector[((j * a) * v)]], Translate[D', Vector[((j * a) * v)]]], j, 1, d) → list11
  45. Sequence(Segment[Translate[F'', Vector[((j * b) * w)]], Translate[D', Vector[((j * b) * w)]]], j, 1, e) → list12
  46. Intersect(xAxis, yAxis) → H
  47. Circle(H, base) → k
  48. Point(k) → I
  49. Line(H, I) → j
  50. OrthogonalLine(H, j) → l
  51. Circle(H, height) → p
  52. Intersect(p, l, 2) → J
  53. OrthogonalLine(J, l) → m
  54. OrthogonalLine(I, j) → n
  55. Intersect(m, n) → K
  56. Polygon(H, I, K, J) → q1, h_1, i_1, k_1, j_1
  57. Angle(H, J, K) → α
  58. Angle(J, K, I) → β
  59. Angle(K, I, H) → γ
  60. Angle(I, H, J) → δ
  61. Angle(H, J, K) → ε
  62. Angle(J, K, I) → ζ
  63. Angle(K, I, H) → η
  64. Angle(I, H, J) → θ

AI Drawing Prompt Reference

Draw a cube and its similar transformed figure. Start by drawing a cube, then apply similarity transformations to its vertices, including dilation, translation, and rotation. Finally, connect the transformed vertices to form new polygons, demonstrating the effect of similarity transformations.
The prompt above was compiled from the original drawing commands and is for reference only.