三角形内角和与外角和定理探索

GeoGebra 命令及参数

1. Ray(A, B) → a
2. Ray(B, C) → b
3. Ray(C, A) → c
4. Point(a) → D_1
5. Point(b) → E_1
6. Point(c) → F_1
7. Ray(A, F_1) → d
8. Ray(B, D_1) → e
9. Ray(C, E_1) → f
10. Point(e) → D
11. Point(f) → E
12. Point(d) → F
13. Angle(B, A, C) → α
14. Angle(C, B, A) → β
15. Angle(A, C, B) → γ
16. Angle(F, A, B) → δ
17. Angle(D, B, C) → ε
18. Angle(E, C, A) → ζ
19. Circle(A, 1.5) → g
20. Circle(B, 1.5) → h
21. Circle(C, 1.5) → k
22. Intersect(g, c, 1) → G
23. Intersect(g, a, 1) → H
24. Intersect(g, c, 2) → I
25. Intersect(h, b, 1) → J
26. Intersect(h, a, 1) → K
27. Intersect(h, a, 2) → L
28. Intersect(k, b) → M, N
29. Intersect(k, c) → O,
30. CircleSector(A, H, G) → p
31. CircleSector(B, J, K) → q
32. CircleSector(C, O, M) → r
33. CircleSector(C, N, O) → s
34. CircleSector(B, L, J) → t
35. CircleSector(A, I, H) → c_1
36. Line(C, a) → i
37. Vector(B, C) → u
38. Vector(A, C) → v
39. Translate(q, u) → q'
40. Dilate(C, If[0 < j ≤ 1, j, 0], B) → C'
41. Vector(B, C') → w
42. Translate(q, w) → q'_1
43. Mirror(q', C) → q''
44. Dilate(A, If[2 < j ≤ 3, 3 - j, 0], C) → C'_1
45. Vector(A, C'_1) → m
46. Translate(p, m) → p'
47. Dilate(C, If[0 < n ≤ 1, n, 0], B) → C'_2
48. Dilate(A, If[1 < n ≤ 2, 2 - n, 0], C) → A'
49. Vector(B, C'_2) → u_1
50. Vector(A, A') → v_1
51. If(0 < n ≤ 1, Translate[t, u_1], Translate[t, u]) → e_1
52. If(1 < n ≤ 2, Translate[c_1, v_1], Translate[c_1, v]) → f_1
53. Polygon(A, B, C) → poly1, c_2, a_2, b_1
54. Line(A, B) → g_1
55. Point(i) → P
56. Point(i) → Q
57. Angle(A, C, B) → η
58. CircleSector(C, M, O) → p_1
59. CircleSector(B, K, J) → q_1
60. CircleSector(A, G, H) → r_1
61. Translate(q_1, w) → s_1
62. Translate(q_1, w) → t_1
63. Vector(B, C) → w_1
64. Translate(q_1, w_1) → e_2
65. Rotate(e_2, 180°, C) → f_2
66. Translate(r_1, m) → g_2
67. CircleSector(C, O, N) → k_2
68. CircleSector(B, J, L) → p_2
69. CircleSector(A, H, I) → q_2
70. Translate(p_2, u_1) → r_2
71. Translate(p_2, u) → s_2
72. Translate(q_2, v_1) → t_2
73. Translate(q_1, u) → d_2
74. Translate(q_1, w) → c_3
75. Translate(A, w) → A'_1
76. Translate(B, w) → B'
77. Translate(C, w) → C'_3
78. Polygon(A'_1, B', C'_3) → poly1', c'_3, a'_1, b'
79. Translate(A, w_1) → A'_2
80. Translate(B, w_1) → B'_1
81. Translate(C, w_1) → C'_4
82. Polygon(A'_2, B'_1, C'_4) → poly1'_1, c'_4, a'_2, b'_1
83. Segment(C'_3, A'_1) → l
84. Segment(A'_1, B') → l_1
85. Segment(B', C'_3) → m_1
86. Segment(C'_4, A'_2) → n_1
87. Segment(A'_2, C'_3) → b_2
88. Segment(C'_3, C'_4) → i_2
89. Rotate(d_2, (((j - 1) * 180))°, C) → h_2
90. Translate(r_1, m) → d_3
91. Translate(A, m) → A'_3
92. Translate(B, m) → B'_2
93. Translate(C, m) → C'_5
94. Polygon(A'_3, B'_2, C'_5) → poly1'_2, c'_5, a'_3, b'_2
95. Segment(B'_2, C'_5) → i_1
96. Segment(C'_5, A'_3) → j_1
97. Segment(A'_3, B'_2) → k_1
98. Line(A, C) → j_2
99. Intersect(k, j_2) → R, S
100. Rotate(S, (((j - 3) * 180))°, C) → S'
101. CircleArc(C, S, S') → e_3
102. Segment(A, B) → l_2
103. Segment(B, C) → m_2
104. Segment(A, C) → n_2
105. Translate(q, w) → d_1
106. Translate(q, u) → q'_2
107. Rotate(q'_2, If[1 < j ≤ 2, (((-(j - 1)) * 180))°, 180°], C) → p''
108. Translate(p, m) → p'_1
109. Rotate(S, (((-(j - 3)) * 180))°, C) → S'_1
110. CircleArc(C, S'_1, S) → f_3
111. Ray(C, A) → a_3