G_8.02 Special right triangles

GeoGebra Commands & Parameters

1. Polygon(A, B, 3) → poly1, a, b, c, C
2. Dilate(A, If[0 < d ≤ 1, 1 - d, 0], B) → A'
3. Segment(A, A') → e
4. Dilate(B, If[1 < d ≤ 2, 2 - d, 0], C) → B'
5. Dilate(C, If[2 < d ≤ 3, 3 - d, 0], A) → C'
6. Segment(A, B) → h
7. Segment(A, C) → i
8. Segment(B, C) → j
9. Circle(A, (0.15 * h)) → k
10. Intersect(k, i, 1) → D
11. Intersect(k, h, 1) → E
12. CircleSector(A, E, D) → p
13. Rotate(A, If[3.5 < d ≤ 4.5, ((d - 3.5) * pi / 3), 1.0471975511965976], A) → A'_1
14. Rotate(A', If[3.5 < d ≤ 4.5, ((d - 3.5) * pi / 3), 1.0471975511965976], A) → A''
15. Segment(A'_1, A'') → e'
16. Rotate(A, If[4.5 < d ≤ 5.5, ((-(d - 4.5)) * pi / 3), -1.0471975511965976], B) → A'_2
17. Rotate(A', If[4.5 < d ≤ 5.5, ((-(d - 4.5)) * pi / 3), -1.0471975511965976], B) → A''_1
18. Segment(A'_2, A''_1) → e'_1
19. Dilate(A, If[6 < d ≤ 7, 7 - d, 0], B) → A'_3
20. Vector(A, A'_3) → u
21. Translate(p, u) → p'
22. Rotate(p', If[7 < d ≤ 8, (((d - 7) * 2) * pi / 3), 2.0943951023931953], B) → p''
23. Circle(B, (0.15 * h)) → r
24. Intersect(r, j, 1) → F
25. Intersect(r, h, 1) → K
26. Dilate(B, If[8 < d ≤ 9, 9 - d, 0], C) → B'_1
27. Vector(B, B'_1) → v
28. Translate(p'', v) → p'''
29. Rotate(p''', If[9 < d ≤ 10, (((d - 9) * 2) * pi / 3), 2.0943951023931953], C) → t
30. Circle(C, (0.15 * h)) → c_1
31. Intersect(c_1, i) → M,
32. Intersect(c_1, j) → N,
33. Midpoint(h) → O
34. Dilate(C, If[10 < d ≤ 11, 11 - d, 0], O) → C'_1
35. Segment(C, C'_1) → l
36. Circle(O, (0.15 * h)) → d_1
37. Intersect(d_1, h) → V_{1}, V_{2}
38. Segment(C, O) → m
39. Intersect(d_1, m, 1) → P
40. Polygon(A, O, C) → poly2, c_2, a_1, o
41. Intersect(c_1, m) → S,
42. CircleSector(C, S, N) → e_1
43. CircleSector(O, V_{2}, P) → f_1
44. Segment(O, B) → n
45. Rotate(e_1, If[13 < d ≤ 14, ((-(d - 13)) * pi / 6), -0.5236], C) → h_1
46. Rotate(O, If[13.25 < d ≤ 14.25, ((-(d - 13.25)) * pi), -3.141592653589793], O) → O'
47. Rotate(B, If[14 < d ≤ 15, ((d - 14) * pi), 3.14159], O) → B'_2
48. Segment(O', B'_2) → n'
49. Segment(O, B) → b_1
50. Dilate(C, If[15 < d ≤ 16, 16 - d, 0], A) → C'_2
51. Vector(C, C'_2) → w
52. Translate(h_1, w) → q_1
53. Dilate(C, If[17 < d ≤ 18, 18 - d, 0], A) → C'_3
54. Vector(C, C'_3) → u_1
55. Translate(h_1, u_1) → s_1
56. Rotate(O', If[19 < d ≤ 20, ((d - 19) * pi / 3), 1.0472], A) → O''
57. Rotate(B'_2, If[18.25 < d ≤ 19.25, ((d - 18.25) * pi / 3), 1.0471975511965976], A) → U
58. Segment(O'', U) → n''
59. Rotate(O'', If[19.25 < d ≤ 20.25, ((d - 19.25) * pi), pi], O'') → O'''
60. Rotate(U, If[20 < d ≤ 21, ((d - 20) * pi), pi], O'') → U'
61. Segment(O''', U') → n'''
62. Rotate(f_1, If[12 < d ≤ 13, ((d - 12) * pi / 2), 1.5708], O) → g_1
63. Rotate(q_1, If[16 < d ≤ 17, (((-(d - 16)) * 4) * pi / 3), -4.18879], A) → r_1
64. Rotate(s_1, If[18 < d ≤ 19, (((-(d - 18)) * 7) * pi / 6), -3.66519], A) → t_1
65. Rotate(E, pi / 6, A) → E'
66. Ray(A, E') → f
67. Circle(A, (0.2 * h)) → q
68. Intersect(q, f, 1) → G
69. Segment(A, G) → g
70. Sequence(Rotate[(1, 0), i°, (0, 0)], i, 15, 360, 15) → list1
71. Segment(H, I) → s
72. Circle(H, I) → k_1
73. OrthogonalLine(H, s) → i_1
74. Intersect(k_1, i_1, 2) → J
75. Intersect(k_1, i_1, 1) → L
76. Dilate(H, If[0 < j_1 ≤ 1, 1 - j_1, 0], I) → H'
77. Segment(H, H') → l_1
78. Rotate(H, If[1 < j_1 ≤ 2, ((j_1 - 1) * pi / 2), pi / 2], H) → H'_{1}
79. Rotate(H', If[1 < j_1 ≤ 2, ((j_1 - 1) * pi / 2), pi / 2], H) → H''
80. Segment(H'_{1}, H'') → m_1
81. Angle(I, H, H'') → α
82. Dilate(J, If[2 < j_1 ≤ 3, 3 - j_1, 0], I) → J'
83. Segment(J, J') → n_1
84. Polygon(H, I, J) → t1, j_2, h_2, i_2
85. Segment(H, I) → p_1
86. Segment(I, J) → f_2
87. Segment(J, H) → g_2
88. Angle(I, H, H'') → β
89. Rotate(f_1, If[12 < d ≤ 13, ((d - 12) * pi / 2), 1.5708], O) → d_2
90. CircleSector(O, V_{2}, P) → e_2
91. Rotate(e_1, If[13 < d ≤ 14, ((-(d - 13)) * pi / 6), -0.5236], C) → k_2
92. CircleSector(A, E, D) → p_2
93. Translate(p, u) → p'_{1}
94. Rotate(p', If[7 < d ≤ 8, (((d - 7) * 2) * pi / 3), 2.0943951023931953], B) → p''_{1}
95. Translate(p'', v) → p'''_{1}
96. Rotate(p''', If[9 < d ≤ 10, (((d - 9) * 2) * pi / 3), 2.0943951023931953], C) → q_2
97. CircleSector(C, S, N) → r_2
98. Translate(h_1, w) → s_2
99. Translate(h_1, w) → t_2
100. Rotate(q_1, If[16 < d ≤ 17, (((-(d - 16)) * 4) * pi / 3), -4.18879], A) → c_3
101. Translate(h_1, u_1) → d_3
102. Rotate(s_1, If[18 < d ≤ 19, (((-(d - 18)) * 7) * pi / 6), -3.66519], A) → e_3
103. Intersect(d_1, m, 1) → T
104. Rotate(C, If[12 < d ≤ 13, ((d - 12) * pi / 2), 1.5708], O) → T'
105. Rotate(B, If[12 < d ≤ 13, ((d - 12) * pi / 2), 1.5708], O) → Q
106. Angle(T', O, Q) → γ
107. Angle(C, O, B) → δ
108. Angle(T', O, Q) → ε
109. Angle(C, O, B) → ζ
110. Segment(A, C) → l_2
111. Segment(A, O) → m_2