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Symmetry Line and Folding

Symmetry Line and Folding
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2016-05-17 19:02
FunctionCalculusTransformationGeometric Construction
This example demonstrates the folding transformation of a figure along a symmetry line and its properties. It involves core mathematical concepts such as symmetry, area, derivative, fractions, fractal geometry, and arithmetic mean. The construction uses commands like Polygon, LineBisector, Segment, Line, Mirror, and Intersect in GeoGebra. Suitable for high school students learning geometric transformations, function graphs, and calculus.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 4) → poly1, f, g, h, i, C, D
  2. LineBisector(D, A) → AD
  3. LineBisector(A, B) → AC
  4. LineBisector(D, B) → AB
  5. LineBisector(C, A) → BD
  6. Segment(E, F) → n
  7. Line(E, F) → studentline
  8. Mirror(D, n) → D'
  9. Mirror(C, n) → C'
  10. Intersect(i, n) → G
  11. Intersect(g, n) → H
  12. Polygon(D', G, H, C') → poly2, d', g_1, h_1, c'
  13. Polygon(A, G, H, B) → poly3, a, g_2, h_2, b
  14. Intersect(n, h) → I
  15. Polygon(I, C', H) → poly4, h_3, i_1, c'_1
  16. Polygon(I, D, A, B, H) → poly5, i_2, d, a_1, b_1, h_4
  17. Polygon(G, D', I) → poly6, i_3, g_3, d'_1
  18. Polygon(G, A, B, C, I) → poly7, g_4, a_2, b_2, c, i_4
  19. Polygon(A, D, C, B) → poly8, a_3, d_1, c_1, b_3
  20. Intersect(n, f) → J
  21. Mirror(A, n) → A'
  22. Polygon(J, A', D', C', H) → poly9, j, a', d'_2, c'_2, h_5
  23. Mirror(B, n) → B'
  24. Polygon(D', G, J, B', C') → poly10, d'_3, g_5, j_1, b', c'_3
  25. Polygon(G, A, J) → poly11, j_2, g_6, a_4
  26. Polygon(J, H, B) → poly12, b_4, j_3, h_6

AI Drawing Prompt Reference

Draw a quadrilateral and find the midpoints of its diagonals to draw the perpendicular bisectors. Reflect the quadrilateral over one of the bisectors to create a folded shape. Then reflect the quadrilateral over the other bisector to create another folded shape. Combine all three shapes to form a symmetric complex figure, demonstrating symmetry and the properties of folding transformations.
The prompt above was compiled from the original drawing commands and is for reference only.