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Dynamic Geometry Problem Example

Dynamic Geometry Problem Example
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2019-01-21 23:20
AngleTransformationGeometric Construction
This is a dynamic and modifiable geometry problem example based on a problem posted by Ed Southall on Twitter. The example demonstrates key mathematical concepts such as angles and geometry. Using GeoGebra commands like Polygon, Ray, Segment, etc., the geometry can be dynamically adjusted to help understand geometric transformations and construction points. Suitable for students and teachers at the middle school level and above.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 12) → poly1, f, p, q, r, C, D, E, F, G, H, I, g, J, K, L, h, i, j, k, l, m, n
  2. Polygon(J, I, 6) → poly2, s, P, t, a, b, c, d, M, N, O
  3. Polygon(I, H, 4) → poly3, e, f_1, g_1, h_1, Q, R
  4. Polygon(E, D, 6) → poly4, i_1, V, j_1, k_1, l_1, m_1, n_1, S, T, U
  5. Ray(Q, N) → p_1
  6. Ray(Q, S) → q_1
  7. Segment(A, B) → r_1
  8. Segment(B, C) → s_1
  9. Segment(C, D) → t_1
  10. Segment(D, E) → a_1
  11. Segment(E, F) → b_1
  12. Segment(F, G) → c_1
  13. Segment(G, H) → d_1
  14. Segment(H, I) → e_1
  15. Segment(I, J) → f_2
  16. Segment(J, K) → g_2
  17. Segment(K, L) → h_2
  18. Segment(L, A) → i_2
  19. Segment(H, Q) → j_2
  20. Segment(Q, R) → k_2
  21. Segment(R, I) → l_2
  22. Segment(R, N) → m_2
  23. Segment(N, O) → n_2
  24. Segment(O, P) → p_2
  25. Segment(P, J) → q_2
  26. Segment(D, S) → r_2
  27. Segment(S, T) → s_2
  28. Segment(T, U) → t_2
  29. Segment(U, V) → a_2
  30. Segment(V, E) → b_2
  31. Semicircle(U, Q) → c_2
  32. Dilate(Q, If[0 < o ≤ 1, 1 - o, 0], N) → Q'
  33. Dilate(Q, If[0 < o ≤ 1, 1 - o, 0], S) → Q'_1
  34. Segment(Q, Q') → d_2
  35. Segment(Q, Q'_1) → e_2
  36. Rotate(V, If[1 < o ≤ 2, (((o - 1) * 2) * π / 3), (2 * π / 3)], U) → V'
  37. Circle(U, (0.5 * a_2)) → c_3
  38. Ray(U, V') → f_3
  39. Intersect(c_3, f_3, 1) → W
  40. Intersect(c_3, a_2, 1) → Z
  41. CircleSector(U, Z, W) → d_3
  42. Rotate(U, If[2.5 < o ≤ 3.5, ((-(o - 2.5)) * π), (-π)], Midpoint[Q, U]) → U'
  43. Vector(U, U') → u
  44. Line(U, d_2) → g_3
  45. Point(g_3) → A_1
  46. Translate(d_3, u) → e_3
  47. Point(g_3) → B_1
  48. Rotate(e_3, If[2.5 < o ≤ 3.5, (((-(o - 2.5)) * 7) * π / 4), (-7 * π / 4)], U') → h_3