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A Curiosity of Right Triangles

A Curiosity of Right Triangles
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2018-03-06 05:05
TriangleCoordinate GeometryGeometric Construction
This example demonstrates a dynamic geometric phenomenon involving the relationship between a square inscribed in a right triangle and its side lengths. Key math concepts include right triangles, squares, coordinate geometry, and continuity. Construction highlights involve GeoGebra commands like Point, Intersect, Segment, OrthogonalLine, Line, Polygon, Midpoint, and Angle. Suitable for high school and above learners exploring geometric properties and functional relationships.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A_2
  2. Point(xAxis) → B_2
  3. Intersect(xAxis, yAxis) → C
  4. Segment(B_2, C) → f
  5. Segment(A_2, C) → g
  6. Segment(B_2, A_2) → h
  7. OrthogonalLine(C, h) → i
  8. Intersect(i, h) → D
  9. Segment(C, D) → j
  10. Segment(A_2, D) → k
  11. Segment(D, B_2) → l
  12. Point(k) → B
  13. Point(l) → A
  14. Point(f) → G
  15. Line(G, l) → m
  16. Intersect(m, g) → H
  17. Segment(G, H) → n
  18. Polygon(A_2, G, C) → d1, c, a, g_1
  19. Polygon(C, H, B_2) → d3, b, c_1, h_1
  20. Segment(L, M) → t
  21. OrthogonalLine(B_2, xAxis) → d
  22. Point(d) → N
  23. Point(d) → O
  24. Segment(N, O) → j_1
  25. Midpoint(t) → P
  26. Midpoint(j_1) → Q
  27. Segment(P, Q) → l_1
  28. OrthogonalLine(A_2, yAxis) → m_1
  29. Point(m_1) → R
  30. Point(m_1) → S
  31. Point(xAxis) → T
  32. Point(xAxis) → U
  33. Segment(T, U) → n_1
  34. Segment(R, S) → p_1
  35. Midpoint(R, S) → V
  36. Midpoint(T, U) → W
  37. Segment(V, W) → q_1
  38. OrthogonalLine(A_2, k) → r_1
  39. OrthogonalLine(B_2, l) → s_1
  40. Point(r_1) → Z
  41. Point(r_1) → A_1
  42. Point(s_1) → B_1
  43. Point(s_1) → C_1
  44. Segment(Z, A_1) → t_1
  45. Segment(B_1, C_1) → a_1
  46. Midpoint(Z, A_1) → D_1
  47. Midpoint(B_1, C_1) → E_1
  48. Segment(D_1, E_1) → b_1
  49. Segment(B, D) → d_1
  50. Segment(D, B_2) → e_1
  51. Angle(D, C, B) → α
  52. Angle(D, A, C) → β
  53. Angle(C, B, D) → γ
  54. Angle(A, C, D) → δ
  55. Angle(B, D, C) → ε
  56. Polygon(B, D, C) → t1, c_2, e, d_2
  57. Polygon(C, D, A) → t2, f_1, c_3, d_3