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Rotational Symmetry of a Square

Rotational Symmetry of a Square
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2018-05-05 06:07
PolygonAngleTransformationGeometric Construction
This example demonstrates the rotational symmetry of a square by rotating it and observing its alignment with the original shape to reveal symmetry. Core mathematical concepts include rotation, symmetry, angles, and polygon construction. It utilizes GeoGebra commands/objects like Circle, Point, Line, OrthogonalLine, Intersect, Polygon, Segment, Angle, and Rotate. Suitable for high school mathematics education to help students visually understand geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Line(A, C) → f
  4. OrthogonalLine(A, f) → g
  5. Intersect(c, g, 2) → D
  6. Polygon(C, D, 4) → poly1, h, i, j, k, E, F
  7. Circle(E, Segment[A, E]) → d
  8. Circle(F, Segment[A, F]) → e
  9. Intersect(d, e, 2) → G
  10. Segment(A, G) → l
  11. Intersect(c, l, 1) → H
  12. Segment(B, A) → m
  13. OrthogonalLine(A, m) → n
  14. Intersect(c, n, 1) → I
  15. Angle(H, A, I) → α
  16. Rotate(B, (-(135°)), A) → B'
  17. Angle(B', A, B) → β
  18. Rotate(B, (-(45°)), A) → B'_1
  19. Angle(B'_1, A, B) → γ
  20. Polygon(B', B'_1, 4) → poly2, p, q, r, s, J, K