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Animation 137: Geometric Transformations and Polygon Demonstration

Animation 137: Geometric Transformations and Polygon Demonstration
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2016-11-06 12:23
FunctionCoordinate GeometrySolid GeometryGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 1) Geometry Review Congruence (Vol 1) Over 80 Resources Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 S N ATTAR CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 Unit 5: Triangle Congruence Triangle Congruence Theorems 1 Triangle Congruence Book 1
This example demonstrates transformations of a cuboid, polygons, and parabola graphs through animation. Core math concepts include vector translation, rotation, polygon construction, function graphing, and parametric equations. Key GeoGebra commands used are Rotate, Vector, Translate, Polygon, and Line as per the construction summary. Suitable for high school and above, ideal for teaching solid geometry, coordinate geometry, and function graphs.

GeoGebra Commands & Parameters

  1. Rotate(B, α, A) → B'
  2. Angle(B, A, B') → β
  3. Ray(A, B') → f
  4. Point(f) → C
  5. Rotate(A, (-γ), B) → A'
  6. Angle(A', B, A) → δ
  7. Ray(B, A') → g
  8. Intersect(f, g) → D
  9. Polygon(A, B, D) → poly1, d, a_1, b
  10. Segment(A, B) → h
  11. Segment(D, B) → i
  12. Segment(D, A) → j
  13. Min({h, i, j}) → c
  14. Circle(A, (0.2 * c)) → e
  15. Circle(B, (0.2 * c)) → k
  16. Intersect(e, h) → E,
  17. Intersect(e, j) → F, I
  18. Intersect(k, h) → G,
  19. Intersect(k, i) → H, J
  20. CircleSector(A, E, F) → p
  21. CircleSector(B, H, G) → q
  22. Rotate(K, β, L) → K'
  23. Angle(K, L, K') → ε
  24. Circle(L, h) → r
  25. Ray(L, K) → m
  26. Intersect(r, m, 1) → M
  27. Ray(L, K') → n
  28. Rotate(L, (-γ), M) → L'
  29. Angle(L', M, L) → ζ
  30. Ray(M, L') → s
  31. Intersect(n, s) → N
  32. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], L) → A'_1
  33. Vector(A, A'_1) → u
  34. Translate(p, u) → p'
  35. Line(L, h) → t
  36. Translate(F, u) → F'
  37. Point(t) → O
  38. Angle(M, L, O) → η
  39. Rotate(p', If[1 < l ≤ 2, ((-(l - 1)) * η), (-η)], L) → p''
  40. Point(t) → P
  41. Angle(P, L, M) → θ
  42. Dilate(B, If[2 < l ≤ 3, 3 - l, 0], L) → B'_1
  43. Vector(B, B'_1) → v
  44. Translate(A, v) → A'_2
  45. Translate(B, v) → B'_2
  46. Segment(A'_2, B'_2) → h'
  47. Rotate(A'_2, If[3 < l ≤ 4, ((l - 3) * θ), θ], L) → Q
  48. Rotate(B'_2, If[3 < l ≤ 4, ((l - 3) * θ), θ], L) → R
  49. Segment(Q, R) → h''
  50. Dilate(B, If[4 < l ≤ 5, 5 - l, 0], M) → B'_3
  51. Vector(B, B'_3) → w
  52. Translate(q, w) → q'
  53. Line(M, g) → f_1
  54. Point(f_1) → S
  55. Angle(N, M, S) → τ
  56. Rotate(q', If[5 < l ≤ 6, ((l - 5) * ((2 * π) - τ)), (2 * π) - τ], M) → q''
  57. Dilate(B, If[6 < l ≤ 7, 7 - l, 0], M) → B'_4
  58. Vector(B, B'_4) → u_1
  59. Translate(A, u_1) → A'_3
  60. Translate(B, u_1) → B'_5
  61. Translate(D, u_1) → D'
  62. Polygon(A'_3, B'_5, D') → poly1', d', a'_3, b'_5
  63. Rotate(A'_3, If[7 < l ≤ 8, ((-(l - 7)) * τ), (-τ)], M) → T
  64. Rotate(B'_5, If[7 < l ≤ 8, ((-(l - 7)) * τ), (-τ)], M) → U
  65. Rotate(D', If[7 < l ≤ 8, ((-(l - 7)) * τ), (-τ)], M) → D''
  66. Polygon(T, U, D'') → poly1'', d'', t_1, u_2