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Animation Demonstrating Congruent Triangles and Rotation

Animation Demonstrating Congruent Triangles and Rotation
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2017-06-04 10:04
TrianglePolygonTransformationGeometric Construction
This example demonstrates the construction and rotation of equilateral triangles through animation, involving core concepts like congruence, rotation, and geometric transformations. It utilizes commands such as Polygon, Segment, Rotate, Min, Line, Intersect, and Dilate in GeoGebra. Suitable for high school mathematics education to understand geometric transformations and properties of figures.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Polygon(C, B, 3) → poly2, d, e, f, D
  3. Polygon(A, C, 3) → poly3, g, h, i, E
  4. Polygon(B, A, 3) → poly4, j, k, l, F
  5. Segment(A, B) → m
  6. Segment(B, C) → n
  7. Segment(C, A) → p
  8. Rotate(B, If[0 < o ≤ 1, (o * π / 3), 1.0471975511965976], B) → B'
  9. Rotate(C, If[0 < o ≤ 1, ((-o) * π / 3), -1.0472], B) → C'
  10. Segment(B', C') → n'
  11. Rotate(B, If[1 < o ≤ 2, ((o - 1) * π / 3), 1.0472], C) → B'_1
  12. Rotate(C, If[0 < o ≤ 1, (o * π / 3), 1.0471975511965976], C) → C'_1
  13. Segment(B'_1, C'_1) → n'_1
  14. Rotate(C, If[2 < o ≤ 3, ((-(o - 2)) * π / 3), -1.0471975511965976], C) → C'_2
  15. Rotate(A, If[2 < o ≤ 3, ((-(o - 2)) * π / 3), -1.0471975511965976], C) → A'
  16. Segment(C'_2, A') → p'
  17. Rotate(C, If[3 < o ≤ 4, ((o - 3) * π / 3), 1.0471975511965976], A) → C'_3
  18. Rotate(A, If[3 < o ≤ 4, ((o - 3) * π / 3), 1.0471975511965976], A) → A'_1
  19. Segment(C'_3, A'_1) → p'_1
  20. Rotate(A, If[4 < o ≤ 5, ((-(o - 4)) * π / 3), -1.0471975511965976], A) → A'_2
  21. Rotate(B, If[4 < o ≤ 5, ((-(o - 4)) * π / 3), -1.0471975511965976], A) → B'_2
  22. Segment(A'_2, B'_2) → m'
  23. Rotate(A, If[5 < o ≤ 6, ((o - 5) * π / 3), 1.0471975511965976], B) → A'_3
  24. Rotate(B, If[5 < o ≤ 6, ((o - 5) * π / 3), 1.0471975511965976], B) → B'_3
  25. Segment(A'_3, B'_3) → m'_1
  26. Min(list1) → t
  27. Rotate(B, π / 3, C) → B'_7
  28. Rotate(A, π / 3, B) → A'_7
  29. Rotate(C, π / 3, A) → C'_7
  30. Line(B'_7, A) → f_1
  31. Line(C, A'_7) → t_1
  32. Line(C'_7, B) → d_1
  33. Intersect(t_1, d_1) → M
  34. Dilate(B'_7, If[6 < o ≤ 7, 7 - o, 0], A) → G
  35. Segment(B'_7, G) → q
  36. Dilate(C'_7, If[7 < o ≤ 8, 8 - o, 0], M) → H
  37. Segment(C'_7, H) → r
  38. Dilate(M, If[8 < o ≤ 9, 9 - o, 0], B) → M'
  39. Segment(M, M') → s
  40. Dilate(A'_7, If[9 < o ≤ 10, 10 - o, 0], M) → I
  41. Segment(A'_7, I) → g_1
  42. Dilate(M, If[10 < o ≤ 11, 11 - o, 0], C) → M'_1
  43. Segment(M, M'_1) → h_1