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Dynamic Illustration of Two Squares with a Common Vertex

Dynamic Illustration of Two Squares with a Common Vertex
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2019-07-26 17:25
PolygonAngleTransformation
This example dynamically illustrates a problem posted by Catriona Shearer on Twitter. It involves two squares that share a common vertex. Using GeoGebra commands such as Polygon, Segment, Circle, Point, etc., the relationship between the squares can be observed intuitively. Suitable for students at the junior high school level and above to learn geometric construction and transformations.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → q1, a_1, b, c, d
  2. Segment(A, B) → f
  3. Segment(B, C) → g
  4. Segment(C, D) → h
  5. Segment(D, A) → i
  6. Circle(D, a) → e
  7. Point(e) → E
  8. Segment(D, E) → j
  9. OrthogonalLine(E, j) → k
  10. Circle(E, a) → p
  11. Intersect(p, k, 2) → F
  12. OrthogonalLine(F, k) → l
  13. OrthogonalLine(D, j) → m
  14. Intersect(e, l, 1) → G
  15. Polygon(D, E, F, G) → q2, d_1, e_1, f_1, g_1
  16. Segment(E, F) → n
  17. Segment(F, G) → q
  18. Segment(G, D) → r
  19. Line(G, C) → s
  20. Line(G, A) → t
  21. Angle(A, G, C) → α
  22. Line(B, D) → h_1
  23. Circle(B, u) → c_1
  24. Intersect(c_1, f, 1) → H
  25. Dilate(G, If[0 < o ≤ 1, 1 - o, 0], A) → G'
  26. Dilate(G, If[0 < o ≤ 1, 1 - o, 0], C) → G'_1
  27. Segment(G, G') → i_1
  28. Segment(G, G'_1) → j_1
  29. Intersect(c_1, xAxis, 2) → I
  30. Rotate(I, π / 4, B) → I'
  31. Ray(B, I') → k_1
  32. Circle(I', B) → p_1
  33. Intersect(p_1, k_1, 2) → J
  34. Dilate(B, If[1 < o ≤ 2, 2 - o, 0], J) → B'
  35. Segment(B, B') → l_1
  36. Rotate(I, If[2.5 < o ≤ 3.5, ((o - 2.5) * π / 4), π / 4], B) → I'_1
  37. CircleSector(B, I, I'_1) → q_1
  38. Rotate(q_1, If[4.5 < o ≤ 5.5, ((o - 4.5) * π / 4), π / 4], B) → r_1
  39. Dilate(B, If[6.5 < o ≤ 7.5, 7.5 - o, 0], G) → B'_1
  40. Vector(B, B'_1) → v
  41. Translate(r_1, v) → s_1
  42. Line(G, l_1) → m_1
  43. Point(m_1) → K
  44. Angle(A, G, K) → β
  45. Rotate(s_1, If[6.5 < o ≤ 7.5, ((-(o - 6.5)) * β), (-β)], B'_1) → t_1
  46. Line(G, C) → n_1
  47. Ray(A, B) → b_1