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Rotational Symmetry of an Isosceles Trapezoid

Rotational Symmetry of an Isosceles Trapezoid
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2016-10-05 00:33
PolygonAngleVectorGeometric Construction
This example demonstrates the rotational symmetry of an isosceles trapezoid. Key math concepts include symmetry, polygons, angles, vectors, and rotational transformations. Construction highlights involve GeoGebra commands like Segment, Line, Circle, Intersect, LineBisector, Polygon, Vector, Angle, and Rotate. Suitable for middle school and above students learning geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(A, C) → g
  3. Line(C, f) → h
  4. Circle(B, Segment[A, C]) → c
  5. Intersect(c, h, 2) → D
  6. Segment(B, D) → i
  7. Segment(D, C) → j
  8. LineBisector(f) → k
  9. LineBisector(g) → m
  10. LineBisector(i) → n
  11. Intersect(m, g) → E
  12. Intersect(n, i) → F
  13. Segment(E, F) → p
  14. Intersect(k, p) → G
  15. Polygon(B, D, C, A) → poly1, b, d, c_1, a
  16. Vector(H, I) → u
  17. Vector(H, J) → v
  18. Angle(J, H, I) → α
  19. Rotate(B, (-α), G) → B'
  20. Rotate(D, (-α), G) → D'
  21. Rotate(C, (-α), G) → C'
  22. Rotate(A, (-α), G) → A'
  23. Polygon(B', D', C', A') → poly1', b', d', c', a'