Exploring Diagonals of an Isosceles Trapezoid

GeoGebra Commands & Parameters

1. Line(A, B_1) → a
2. Ray(A, B_1) → b
3. Point(b) → B
4. Midpoint(A, B) → D_1
5. Line(A, B) → c
6. Slope(c) → d
7. OrthogonalLine(D_1, c) → g
8. Point(g) → E_1
9. Ray(D_1, E_1) → h
10. Point(h) → F
11. Slope(h) → i
12. Line(F, c) → l
13. Point(l) → G
14. Point(l) → H
15. Ray(F, G) → m
16. Ray(F, H) → n
17. Point(m) → D
18. Mirror(D, h) → I'
19. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
20. Segment(A, A') → p
21. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], D) → A'_1
22. Segment(A, A'_1) → q
23. Segment(A, B) → r
24. Segment(B, I') → s
25. Segment(I', D) → t
26. Segment(D, A) → a_1
27. Circle(A, (0.2 * Min[a_1, r])) → c_1
28. Circle(D, (0.2 * Min[a_1, r])) → d_1
29. Intersect(d_1, a_1, 1) → J
30. Intersect(d_1, t, 1) → K
31. Intersect(c_1, r, 1) → L
32. Intersect(c_1, a_1, 1) → M
33. Dilate(D, If[2 < o ≤ 3, 3 - o, 0], I') → I'_1
34. Segment(D, I'_1) → b_1
35. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], B) → A'_2
36. Vector(A, A'_2) → u
37. Translate(A, u) → A'_3
38. Translate(A'_1, u) → N
39. Segment(A'_3, N) → q'
40. OrthogonalLine(A, r) → g_1
41. Point(g_1) → O
42. Angle(D, A, O) → α
43. Angle(I', B, A) → β
44. Rotate(A'_3, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], B) → P
45. Rotate(N, If[4 < o ≤ 5, (((o - 4) * 2) * α), (2 * α)], B) → C
46. Segment(P, C) → q''
47. Dilate(A, If[5 < o ≤ 6, 6 - o, 0], B) → A'_4
48. Vector(A, A'_4) → v
49. Dilate(D, If[7 < o ≤ 8, 8 - o, 0], I') → I'_2
50. Vector(D, I'_2) → w
51. Dilate(A, If[9 < o ≤ 10, 10 - o, 0], I') → A'_5
52. Segment(A, A'_5) → i_1
53. Dilate(A, If[10 < o ≤ 11, 11 - o, 0], D) → A'_6
54. Vector(A, A'_6) → u_1
55. Translate(A, u_1) → A'_7
56. Translate(A'_5, u_1) → Q
57. Segment(A'_7, Q) → j_1
58. Segment(D, B) → l_1
59. Angle(L, A, I') → γ
60. Rotate(A'_7, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → R
61. Rotate(Q, If[11 < o ≤ 12, ((-(o - 11)) * (2 * γ)), (-2 * γ)], D) → Q'
62. Segment(R, Q') → m_1
63. Polygon(A, B, I', D) → poly1, a_2, c_2, i', i_2
64. Intersect(i_1, m_1) → E
65. Distance(A, E) → distanceAS
66. Distance(E, C) → distanceSN'
67. Distance(E, B) → distanceSC
68. Distance(E, D) → distanceSI
69. Angle(B, A, E) → δ
70. Angle(E, B, A) → ε
71. Angle(C, B, E) → ζ
72. Angle(E, A, D) → η
73. Angle(A, D, E) → θ
74. Angle(E, D, C) → ι
75. Angle(D, C, E) → κ
76. Angle(B, E, C) → λ
77. Angle(E, C, B) → μ
78. Angle(A, E, B) → ν
79. Polygon(A, B, C) → poly2, c_3, a_3, b_2
80. Segment(A, C) → h_1
81. Mirror(A, h_1) → A'_8
82. Mirror(B, h_1) → B'
83. Mirror(C, h_1) → C'
84. Polygon(A'_8, B', C') → poly2', c', a'_8, b'
85. Polygon(D, A, B) → poly3, b_3, d_2, a_4
86. Segment(D, B) → p_1
87. Mirror(D, p_1) → D'
88. Mirror(A, p_1) → A'_9
89. Mirror(B, p_1) → B'_1
90. Polygon(D', A'_9, B'_1) → poly3', b'_1, d', a'_9