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Rotational Symmetry of an Equilateral Triangle

Rotational Symmetry of an Equilateral Triangle
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2019-02-26 07:42
TrianglePolygonTransformation
This example demonstrates the rotational symmetry of an equilateral triangle. Key mathematical concepts include rotation symmetry and geometric transformations. Using the Rotate command, users can observe how the equilateral triangle changes at different rotation angles. The key commands used in the construction include Rotate, Angle, Segment, LineBisector, Intersect, Circle, and Polygon. Suitable for middle school and above students to learn about geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Rotate(A, 59.99999999999999°, B) → A'
  2. Angle(A, B, A') → α
  3. Segment(B, A) → a
  4. Segment(B, A') → b
  5. Rotate(B, 300.00000000000006°, A) → B'
  6. Angle(B, A, B') → β
  7. Segment(A, B') → c
  8. LineBisector(a) → d
  9. LineBisector(c) → e
  10. Intersect(d, e) → C
  11. Circle(C, A) → f
  12. Polygon(A, A', B) → poly1, b_1, a_1, a'
  13. Rotate(A, Angle, C) → A'_1
  14. Rotate(A', Angle, C) → A''
  15. Rotate(B, Angle, C) → B'_1
  16. Polygon(A'_1, A'', B'_1) → poly1', b'_1, a'_1, a''