Investigating Similar Quadrilaterals

GeoGebra Commands & Parameters

1. Polygon(A, B, 4) → poly1, a, b, c, d, C, D
2. Line(A, B) → e
3. Slope(e) → f
4. Ray(A, B) → i
5. Point(i) → E
6. Ray(B, E) → j
7. Point(j) → F
8. Circle(F, Distance[A, B]) → k
9. Distance(A, B) → l
10. Circle(F, l) → p
11. Intersect(p, j, 2) → G
12. Intersect(p, j, 1) → H
13. CircleArc(F, G, H) → q
14. Point(q) → I
15. Circle(I, l) → r
16. Circle(G, l) → s
17. Intersect(r, s, 1) → J
18. Line(A, B) → n
19. Line(K, n) → t
20. Point(t) → M
21. Circle(K, l) → c_1
22. Intersect(c_1, t, 2) → L
23. Intersect(c_1, t, 1) → N
24. CircleArc(K, L, N) → d_1
25. Point(d_1) → O
26. Angle(M, K, O) → α
27. Segment(K, O) → m
28. Sequence(Dilate[O, If[0 < o ≤ 1, 1 - o, 0], Element[list1, i]], i, 1, 8, 1) → list2
29. Sequence(Vector[O, Element[list2, i]], i, 1, 8, 1) → list3
30. Dilate(O, If[0 < o ≤ 1, 1 - o, 0], A) → O'
31. Dilate(O, If[0 < o ≤ 1, 1 - o, 0], B) → O'_1
32. Dilate(O, If[0 < o ≤ 1, 1 - o, 0], C) → O'_2
33. Dilate(O, If[0 < o ≤ 1, 1 - o, 0], D) → O'_3
34. Dilate(O, If[0 < o ≤ 1, 1 - o, 0], F) → O'_4
35. Dilate(O, If[0 < o ≤ 1, 1 - o, 0], G) → O'_5
36. Dilate(O, If[0 < o ≤ 1, 1 - o, 0], J) → O'_6
37. Dilate(O, If[0 < o ≤ 1, 1 - o, 0], I) → O'_7
38. Vector(O, O') → u
39. Vector(O, O'_1) → v
40. Vector(O, O'_2) → w
41. Vector(O, O'_3) → u_1
42. Vector(O, O'_4) → v_1
43. Vector(O, O'_5) → w_1
44. Vector(O, O'_6) → a_1
45. Vector(O, O'_7) → b_1
46. Translate(K, u) → K'
47. Translate(O, u) → O'_8
48. Segment(K', O'_8) → m'
49. Translate(K, u_1) → K'_1
50. Translate(O, u_1) → O'_9
51. Segment(K'_1, O'_9) → m'_1
52. Translate(K, w) → K'_2
53. Translate(O, w) → O'_{10}
54. Segment(K'_2, O'_{10}) → m'_2
55. Translate(K, v) → K'_3
56. Translate(O, v) → O'_{11}
57. Segment(K'_3, O'_{11}) → m'_3
58. Translate(K, b_1) → K'_4
59. Translate(O, b_1) → O'_{12}
60. Segment(K'_4, O'_{12}) → m'_4
61. Translate(K, a_1) → K'_5
62. Translate(O, a_1) → O'_{13}
63. Segment(K'_5, O'_{13}) → m'_5
64. Translate(K, v_1) → K'_6
65. Translate(O, v_1) → O'_{14}
66. Segment(K'_6, O'_{14}) → m'_6
67. Translate(K, w_1) → K'_7
68. Translate(O, w_1) → O'_{15}
69. Segment(K'_7, O'_{15}) → m'_7
70. Rotate(K'_6, If[1 < o ≤ 2, ((o - 1) * (π - α)), π - α], F) → P
71. Rotate(O'_{14}, If[1 < o ≤ 2, ((o - 1) * (π - α)), π - α], F) → Q
72. Segment(P, Q) → e_1
73. Rotate(K'_4, If[1 < o ≤ 2, ((o - 1) * α), α], I) → R
74. Rotate(O'_{12}, If[1 < o ≤ 2, ((o - 1) * α), α], I) → S
75. Line(I, F) → g_1
76. Line(I, m'_6) → h_1
77. Point(h_1) → T
78. Point(g_1) → U
79. Ray(I, T) → i_1
80. Ray(I, U) → j_1
81. Ray(I, T) → k_1
82. Ray(I, U) → l_1
83. Point(k_1) → V
84. Point(l_1) → W
85. Angle(V, I, W) → β
86. Rotate(K'_4, If[1 < o ≤ 2, ((o - 1) * β), β], I) → Z
87. Rotate(O'_{12}, If[1 < o ≤ 2, ((o - 1) * β), β], I) → A_1
88. Segment(Z, A_1) → m_1
89. Rotate(K'_5, If[1 < o ≤ 2, ((o - 1) * β), β], J) → B_1
90. Rotate(O'_{13}, If[1 < o ≤ 2, ((o - 1) * β), β], J) → C_1
91. Rotate(K'_5, If[1 < o ≤ 2, ((o - 1) * ((2 * π) - α)), (2 * π) - α], J) → D_1
92. Rotate(O'_{13}, If[1 < o ≤ 2, ((o - 1) * ((2 * π) - α)), (2 * π) - α], J) → E_1
93. Segment(D_1, E_1) → f_1
94. Rotate(K'_7, If[1 < o ≤ 2, ((o - 1) * (π + β)), π + β], G) → F_1
95. Rotate(O'_{15}, If[1 < o ≤ 2, ((o - 1) * (π + β)), π + β], G) → G_1
96. Segment(F_1, G_1) → n_1
97. Rotate(K'_3, If[1 < o ≤ 2, ((-(o - 1)) * α), (-α)], B) → H_1
98. Rotate(O'_{11}, If[1 < o ≤ 2, ((-(o - 1)) * α), (-α)], B) → I_1
99. Segment(H_1, I_1) → p_1
100. Rotate(K', If[1 < o ≤ 2, ((-(o - 1)) * (π / 2 + α)), (-(π / 2 + α))], A) → K''
101. Rotate(O'_8, If[1 < o ≤ 2, ((-(o - 1)) * (π / 2 + α)), (-(π / 2 + α))], A) → J_1
102. Segment(K'', J_1) → m''
103. Rotate(K'_1, If[1 < o ≤ 2, ((-(o - 1)) * (π + α)), (-(π + α))], D) → K_1
104. Rotate(O'_9, If[1 < o ≤ 2, ((-(o - 1)) * (π + α)), (-(π + α))], D) → L_1
105. Segment(K_1, L_1) → q_1
106. Rotate(K'_2, If[1 < o ≤ 2, ((-(o - 1)) * ((3 * π / 2) + α)), (-((3 * π / 2) + α))], C) → M_1
107. Rotate(O'_{10}, If[1 < o ≤ 2, ((-(o - 1)) * ((3 * π / 2) + α)), (-((3 * π / 2) + α))], C) → N_1
108. Segment(M_1, N_1) → r_1
109. Polygon(A, B, C, D) → poly2, a_2, b_2, c_2, d_2
110. Polygon(F, G, J, I) → poly3, f_2, g_2, j_2, i_2