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Point and Rotational Symmetry by Joy

Point and Rotational Symmetry by Joy
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2016-07-29 01:12
PolygonTransformationGeometric Construction
This example demonstrates point and rotational symmetry in geometric figures. It involves core concepts like symmetry, rotation, isosceles triangles, parallelograms, congruence, and quadrilaterals. The construction uses commands such as Polygon, Midpoint, Segment, Intersect, Rotate, Angle, and Point. Suitable for middle school and above students to understand geometric transformations and symmetry properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, a, a_1, b, C
  2. Midpoint(a) → D
  3. Midpoint(a_1) → E
  4. Segment(A, E) → c
  5. Segment(D, C) → d
  6. Intersect(c, d) → F
  7. Rotate(A, α, F) → A'
  8. Rotate(B, α, F) → B'
  9. Rotate(C, α, F) → C'
  10. Polygon(A', B', C') → poly1', c', a', b'
  11. Polygon(G, H, I, J) → poly2, g, h, i, j
  12. Segment(G, I) → e
  13. Segment(J, H) → f
  14. Intersect(e, f) → K
  15. Rotate(G, α, K) → G'
  16. Rotate(H, α, K) → H'
  17. Rotate(I, α, K) → I'
  18. Rotate(J, α, K) → J'
  19. Polygon(G', H', I', J') → poly2', g', h', i', j'
  20. Rotate(pic1, α, L) → pic1'
  21. Polygon(M, N, 5) → poly3, m_1, n, p, q, r, O, P, Q
  22. Midpoint(p) → R
  23. Midpoint(n) → S
  24. Segment(Q, S) → s
  25. Segment(M, R) → t
  26. Intersect(t, s) → T
  27. Rotate(M, α, T) → M'
  28. Rotate(N, α, T) → N'
  29. Rotate(O, α, T) → O'
  30. Rotate(P, α, T) → P'
  31. Rotate(Q, α, T) → Q'
  32. Polygon(M', N', O', P', Q') → poly3', m', n', o', p', q'
  33. Angle(B, A, C) → β
  34. Angle(B', A', C') → γ
  35. Angle(H, G, J) → δ
  36. Angle(H', G', J') → ε
  37. Segment(G', I') → b_1
  38. Segment(J', H') → c_1
  39. Intersect(c_1, b_1) → U
  40. Angle(N', M', Q') → ζ
  41. Angle(N, M, Q) → η
  42. Segment(T, M') → d_1
  43. Point(d_1) → V
  44. Segment(V, N') → e_1
  45. Segment(V, O') → f_1
  46. Segment(V, P') → g_1
  47. Segment(V, Q') → h_1