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Symmetry Lines of a Square

Symmetry Lines of a Square
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2016-01-13 07:25
PolygonTransformationGeometric Construction
This example demonstrates the four lines of symmetry in a square. It involves core mathematical concepts such as symmetry, geometric transformations, and polygon properties. The construction uses GeoGebra commands/objects like Polygon, Line, LineBisector, Intersect, Mirror, Midpoint, Segment, and If. Suitable for middle school students and teachers learning geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a_1, b_1, d_1, c_1
  2. Line(C, B) → j
  3. Line(D, C) → k
  4. Line(A, B) → l
  5. Line(D, A) → m
  6. LineBisector(M, C) → c
  7. Intersect(c, k) → F_1
  8. Intersect(c, l) → G
  9. Intersect(c, m) → H
  10. Intersect(j, c) → I
  11. Mirror(B, c) → B'
  12. Mirror(D, c) → D'
  13. Mirror(A, c) → A'
  14. Polygon(M, F_1, I) → poly2, i, e, f
  15. Polygon(F_1, D, A, B, I) → poly3, f_1, d, a_2, b_2, i_1
  16. Polygon(F_1, M, B', G) → poly4, f_2, e_1, b', g
  17. Polygon(F_1, D, A, G) → poly5, f_3, d_2, a_3, g_1
  18. Polygon(F_1, M, B', A', H) → poly6, f_4, e_2, b'_1, a', h
  19. Polygon(F_1, D, H) → poly7, h_1, f_5, d_3
  20. Polygon(H, D', M, I) → poly8, h_2, d', e_3, i_2
  21. Polygon(H, A, B, I) → poly9, h_3, a_4, b_3, i_3
  22. Polygon(H, D', M, B', G) → poly10, h_4, d'_1, e_4, b'_2, g_2
  23. Polygon(H, A, G) → poly11, g_3, h_5, a_5
  24. Polygon(G, B, I) → poly13, i_4, g_4, b_4
  25. Polygon(G, A', D', M, I) → poly12, n, p, q, r, s
  26. Midpoint(D, C) → E
  27. Midpoint(A, B) → F
  28. Segment(E, F) → t
  29. If(Distance[M, D] ≤ 0.05, 1, 0) → ok
  30. Midpoint(C, M) → J
  31. Midpoint(b_1) → K
  32. Midpoint(c_1) → L
  33. Line(L, K) → a1
  34. Line(E, F) → b1
  35. Line(D, B) → b
  36. Line(D, B) → c1
  37. Line(C, A) → d1

AI Drawing Prompt Reference

Draw a square and display its four lines of symmetry. Start by drawing the square, then find the midpoint of each side and draw lines connecting these midpoints to the opposite vertices of the square; these lines are the symmetry axes. Next, reflect parts of the square across each symmetry axis to create multiple smaller shapes. Finally, display the complex pattern formed by the original square and the reflected shapes.
The prompt above was compiled from the original drawing commands and is for reference only.