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Equilateral Triangle Reflection

Equilateral Triangle Reflection
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2016-07-12 00:06
TriangleVectorTransformation
This example demonstrates the reflection transformation of an equilateral triangle. Key mathematical concepts include reflection and geometric transformations. Using GeoGebra commands such as Polygon, Segment, Vector, Translate, etc., the construction of an equilateral triangle and its reflection transformation is illustrated. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. Segment(A, C) → i
  3. Segment(C, B) → j
  4. Segment(B, A) → k
  5. Vector(D, E) → u
  6. Vector(F, G) → v
  7. Translate(A, u) → A'
  8. Translate(C, u) → C'
  9. Segment(A', C') → i'
  10. Translate(C, u) → C'_1
  11. Translate(B, u) → B'
  12. Segment(C'_1, B') → j'
  13. Translate(B, u) → B'_1
  14. Translate(A, u) → A'_1
  15. Segment(B'_1, A'_1) → k'
  16. Translate(A, v) → A'_2
  17. Translate(C, v) → C'_2
  18. Segment(A'_2, C'_2) → i'_1
  19. Translate(C, v) → C'_3
  20. Translate(B, v) → B'_2
  21. Segment(C'_3, B'_2) → j'_1
  22. Translate(B, v) → B'_3
  23. Translate(A, v) → A'_3
  24. Segment(B'_3, A'_3) → k'_1
  25. LineBisector(A, B) → l
  26. LineBisector(A', C') → m
  27. LineBisector(C'_2, B'_2) → n
  28. Intersect(l, k) → H
  29. Polygon(A, H, C) → poly2, c, a, h_1
  30. Intersect(m, i') → I
  31. Polygon(C', I, B') → poly3, b', c', i_1
  32. Intersect(n, j'_1) → J
  33. Polygon(A'_2, C'_2, J) → poly4, j_1, a'_2, c'_2