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Inner Parallelogram Animation

Inner Parallelogram Animation
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2019-09-02 22:33
PolygonTransformationGeometric ConstructionSlider Animation
In collections Exploring Feyman's Triangle
This example demonstrates the animation of an inner parallelogram. Key mathematical concepts include the properties of parallelograms, line intersections, segments, midpoints, polygons, and rotations. Using GeoGebra commands such as Line, Intersect, Segment, Midpoint, Polygon, and Rotate, the construction process of the parallelogram is dynamically shown. Suitable for middle school and above students to learn geometric transformations and dynamic geometry.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(B, C) → g
  3. Line(A, g) → h
  4. Line(C, f) → i
  5. Intersect(h, i) → D
  6. Segment(B, A) → j
  7. Segment(A, D) → k
  8. Segment(D, C) → l
  9. Segment(C, B) → m
  10. Midpoint(j) → M
  11. Midpoint(k) → P
  12. Midpoint(l) → O
  13. Midpoint(m) → N
  14. Segment(A, N) → n
  15. Segment(P, C) → p
  16. Segment(B, O) → q
  17. Segment(M, D) → r
  18. Intersect(n, r) → F
  19. Intersect(p, r) → E
  20. Intersect(p, q) → H
  21. Intersect(n, q) → G
  22. Polygon(A, M, F) → t1, f_1, a, m_1
  23. Rotate(A, α, M) → A'
  24. Rotate(M, α, M) → M'
  25. Rotate(F, α, M) → F'
  26. Polygon(A', M', F') → t1', f', a', m'
  27. Polygon(P, E, D) → t2, d, p_1, e
  28. Rotate(P, α, P) → P'
  29. Rotate(E, α, P) → E'
  30. Rotate(D, α, P) → D'
  31. Polygon(P', E', D') → t2', d', p', e'
  32. Polygon(H, O, C) → t3, c, h_1, o
  33. Polygon(G, N, B) → t4, b, g_1, n_1
  34. Rotate(H, α, O) → H'
  35. Rotate(O, α, O) → O'
  36. Rotate(C, α, O) → C'
  37. Polygon(H', O', C') → t3', c', h', o'
  38. Rotate(G, α, N) → G'
  39. Rotate(N, α, N) → N'
  40. Rotate(B, α, N) → B'
  41. Polygon(G', N', B') → t4', b', g', n'
  42. Polygon(A, F, E, P) → q1, a_1, f_2, e_1, p_2
  43. Polygon(D, E, H, O) → q2, d_1, e_2, h_2, o_1
  44. Polygon(H, C, N, G) → q3, h_3, c_1, n_2, g_2
  45. Polygon(F, M, B, G) → q4, f_3, m_2, b_1, g_3

AI Drawing Prompt Reference

Draw an animated inner parallelogram showing the rotation of its sides, vertices, and midpoints. Start by drawing two line segments to establish the base sides, then find their intersection to form the fourth side of the parallelogram. Calculate the midpoints of each side and connect them to create a new quadrilateral. Use a slider to control the rotation angle, dynamically demonstrating the rotation of the parallelogram and its inner shape, highlighting geometric transformations and symmetry.
The prompt above was compiled from the original drawing commands and is for reference only.