Octagon Interior & Exterior Angle Sum Theorems

GeoGebra Commands & Parameters

1. Ray(S_1, D) → i_5
2. Circle(D, 1.5) → k
3. Intersect(k, i_5) → U_1, V_1
4. Ray(D, A_1) → a_3
5. Intersect(k, a_3, 1) → D_1
6. Segment(C, A_1) → i_3
7. Circle(C, 1.5) → h
8. Intersect(h, i_3) → L,
9. Ray(C, D) → c
10. Intersect(h, c, 1) → P
11. Ray(A, B) → a
12. Ray(B, C) → b
13. Ray(E, A) → e
14. Circle(A, 1.5) → f
15. Circle(B, 1.5) → g
16. Circle(E, 1.5) → p
17. Segment(C, A) → i
18. Segment(C, E) → j
19. Intersect(f, a, 1) → F
20. Intersect(f, i, 1) → G
21. Intersect(f, e, 1) → H
22. Intersect(f, e, 2) → I
23. Intersect(p, e) → J,
24. Intersect(p, j) → K,
25. Intersect(k, c, 2) → O
26. Intersect(h, j, 1) → Q
27. Intersect(h, i, 1) → R
28. Intersect(h, b, 1) → S
29. Intersect(g, a, 2) → T
30. Intersect(g, b, 1) → U
31. Intersect(g, a, 1) → V
32. CircleSector(A, F, G) → q
33. CircleSector(A, G, H) → r
34. CircleSector(B, U, V) → s
35. CircleSector(C, Q, R) → c_1
36. CircleSector(C, R, S) → d_1
37. Intersect(k, c, 1) → W
38. CircleSector(E, J, K) → h_1
39. CircleSector(A, I, F) → p_1
40. CircleSector(B, T, U) → q_1
41. Intersect(h, b, 2) → Z
42. Vector(A, B) → u
43. Vector(C, B) → v
44. Vector(E, D) → w
45. Vector(C, D) → u_1
46. Vector(C, E) → v_1
47. Vector(A, E) → w_1
48. Translate(q, u) → q'
49. Translate(d_1, v) → s_1
50. Mirror(s_1, B) → t_1
51. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], B) → A'
52. Dilate(C, If[0 < l ≤ 1, 1 - l, 0], B) → C'
53. Dilate(A, If[1 < l ≤ 2, 2 - l, 0], E) → A'_1
54. Dilate(C, If[1 < l ≤ 2, 2 - l, 0], E) → C'_1
55. Dilate(C, If[2 < l ≤ 3, 3 - l, 0], D) → C'_2
56. Dilate(E, If[2 < l ≤ 3, 3 - l, 0], D) → E'
57. Vector(A, B) → a_1
58. Vector(C, C') → b_1
59. Vector(A, A'_1) → i_1
60. Vector(E, E') → j_1
61. Vector(C, C'_2) → l_1
62. Vector(C, C'_1) → m_1
63. Translate(d_1, b_1) → c_2
64. Translate(r, i_1) → r'_1
65. Translate(r, w_1) → r'_2
66. Translate(c_1, v_1) → f_2
67. Translate(c_1, m_1) → g_2
68. CircleSector(C, P, L) → t
69. Translate(t, u_1) → t'
70. Translate(t, l_1) → t'_1
71. Translate(q, a_1) → r'
72. Translate(d_1, b_1) → h_2
73. If(0 < l < 1, Rotate[h_2, ((l * 180))°, C']) → k_2
74. Vector(A, A') → n_1
75. Translate(q, n_1) → q'_1
76. Mirror(r'_2, E) → p_2
77. If(1 < l < 2, Rotate[r'_1, (((l - 1) * 180))°, A'_1]) → q_2
78. Segment(E, C) → i_2
79. Vector(D, C) → u_2
80. Vector(E, C) → v_2
81. Vector(A, C) → w_2
82. Vector(B, C) → l_2
83. Dilate(B, If[0 < o < 1, 1 - o, 0], C) → B'
84. Dilate(A, If[1 < o < 2, 2 - o, 0], C) → A'_2
85. Dilate(E, If[2 < o < 3, 3 - o, 0], C) → E'_1
86. Dilate(D, If[3 < o < 4, 4 - o, 0], C) → D'
87. Vector(B, B') → m_2
88. Vector(A, A'_2) → n_2
89. Vector(E, E'_1) → s_2
90. Vector(D, D') → t_2
91. Translate(q_1, m_2) → c_3
92. Translate(q_1, l_2) → d_3
93. Translate(p_1, w_2) → e_3
94. If(1 < o < 2, Translate[p_1, n_2]) → h_3
95. Ray(A_1, E) → b_3
96. Circle(A_1, 1.5) → q_3
97. Intersect(q_3, i_3) → M,
98. Intersect(q_3, b_3, 1) → N
99. Intersect(q_3, a_3, 2) → B_1
100. Intersect(k, c, 2) → C_1
101. Intersect(k, c, 1) → E_1
102. CircleSector(C, L, Q) → d
103. Intersect(p, b_3, 1) → F_1
104. Intersect(p, i_2) → G_1,
105. CircleSector(E, G_1, N) → e_1
106. Dilate(E, If[2 < l < 3, 3 - l, 0], A_1) → E'_2
107. Dilate(C, If[2 < l < 3, 3 - l, 0], A_1) → C'_3
108. Dilate(C, If[3 < l < 4, 4 - l, 0], D) → C'_4
109. Dilate(A_1, If[3 < l < 4, 4 - l, 0], D) → H_1
110. Vector(E, A_1) → f_1
111. Vector(C, A_1) → g_1
112. Translate(e_1, f_1) → k_1
113. Translate(d, g_1) → d'
114. Vector(E, E'_2) → a_2
115. Vector(C, C'_3) → b_2
116. Translate(e_1, a_2) → d_2
117. Translate(d, b_2) → d'_1
118. Rotate(d_2, If[2 < l < 3, (((l - 2) * 180))°, 0], E'_2) → e_2
119. Mirror(k_1, A_1) → r_2
120. CircleSector(A_1, N, M) → f_3
121. Intersect(q_3, a_3, 1) → I_1
122. CircleSector(A_1, M, I_1) → g_3
123. CircleSector(D, D_1, E_1) → k_3
124. Vector(C, D) → j_2
125. Vector(A_1, D) → u_3
126. Translate(g_3, u_3) → p_3
127. Translate(t, j_2) → t'_2
128. Mirror(p_3, D) → r_3
129. Vector(A_1, H_1) → v_3
130. Vector(C, C'_4) → w_3
131. Translate(g_3, v_3) → s_3
132. Translate(t, w_3) → t'_3
133. Rotate(s_3, If[3 < l < 4, (((l - 3) * 180))°, 0], H_1) → t_3
134. Intersect(p, b_3, 2) → J_1
135. Polygon(A, B, C) → poly1, c_4, a_4, b_4
136. Polygon(A, C, E) → poly2, e_4, a_5, c_5
137. Polygon(E, C, A_1) → poly3, a_6, e_5, c_6
138. Polygon(A_1, C, D) → poly4, d_4, a_7, c_7
139. Intersect(p, e, 1) → L_1
140. CircleSector(E, J_1, L_1) → f_4
141. CircleSector(A_1, B_1, N) → g_4
142. Vector(E, C) → j_3
143. Vector(A_1, C) → l_3
144. Vector(D, C) → m_3
145. Translate(f_4, j_3) → k_4
146. Translate(g_4, l_3) → p_4
147. CircleSector(D, V_1, D_1) → h_4
148. Translate(h_4, m_3) → q_4
149. Dilate(E, If[2 < o < 3, 3 - o, 0], C) → E'_3
150. Dilate(A_1, If[3 < o < 4, 4 - o, 0], C) → M_1
151. Dilate(D, If[4 < o < 5, 5 - o, 0], C) → D'_1
152. Vector(E, E'_3) → n_3
153. Vector(A_1, M_1) → u_4
154. Vector(D, D'_1) → v_4
155. If(2 < o < 3, Translate[f_4, n_3]) → r_4
156. If(3 < o < 4, Translate[g_4, u_4]) → s_4
157. If(4 < o < 5, Translate[h_4, v_4]) → t_4
158. Ray(C, N_1) → i_4
159. Ray(N_1, D) → l_4
160. Circle(N_1, 1.5) → d_5
161. Intersect(d_5, i_4, 2) → K_1
162. Intersect(d_5, l_4, 1) → O_1
163. Intersect(d_5, i_4, 1) → P_1
164. Intersect(h, i_4, 1) → Q_1
165. Intersect(k, l_4, 1) → R_1
166. Dilate(D, If[4 < l < 5, 5 - l, 0], N_1) → D'_2
167. Dilate(C, If[4 < l < 5, 5 - l, 0], N_1) → C'_5
168. Vector(C, N_1) → w_4
169. Vector(D, N_1) → j_4
170. Vector(D, D'_2) → m_4
171. Vector(C, C'_5) → n_4
172. Ray(N_1, S_1) → b_5
173. Segment(D, C) → j_5
174. Intersect(d_5, b_5) → T_1,
175. Dilate(D, If[5 < l < 6, 6 - l, 0], S_1) → D'_3
176. Dilate(N_1, If[5 < l < 6, 6 - l, 0], S_1) → W_1
177. Vector(D, D'_3) → u_5
178. Vector(N_1, W_1) → v_5
179. Vector(D, S_1) → w_5
180. Vector(N_1, S_1) → m_5
181. Circle(S_1, 1.5) → r_6
182. Intersect(r_6, i_5, 1) → Z_1
183. Intersect(r_6, b_5) → A_2, B_2
184. Polygon(A, B, C, N_1, S_1, D, A_1, E) → poly7, a_8, b_6, c_9, n_7, s_7, d_8, a_9, e_8
185. CircleSector(C, Z, Q_1) → r_1
186. CircleSector(W_1, B_2, Z_1) → h_7
187. CircleSector(N_1, K_1, T_1) → k_7
188. Vector(W_1, C) → u_6
189. Vector(N_1, C) → v_6
190. Translate(h_7, u_6) → p_7
191. Vector(D, C) → w_6
192. Translate(h_4, w_6) → q_7
193. Dilate(W_1, If[5 < o < 6, 6 - o, 0], C) → C_2
194. Vector(W_1, C_2) → i_6
195. Translate(h_7, i_6) → r_7
196. Dilate(N_1, If[6 < o < 7, 7 - o, 0], C) → D_2
197. Vector(N_1, D_2) → j_6
198. Translate(k_7, j_6) → t_7
199. Vector(N_1, C) → l_6
200. Translate(k_7, l_6) → f_8
201. Ray(C, D) → m_6
202. Ray(C, A_1) → b_7
203. Ray(C, E) → i_7
204. Point(i_7) → E_2
205. Point(b_7) → F_2
206. Point(m_6) → G_2
207. Ray(E, E_2) → j_7
208. Ray(A_1, F_2) → l_7
209. Ray(D, G_2) → m_7
210. Segment(C, S_1) → l_5
211. Intersect(k, i_5, 1) → H_2
212. Intersect(d_5, b_5, 1) → I_2
213. CircleSector(N_1, I_2, P_1) → g_5
214. Intersect(r_6, l_5) → J_2,
215. Intersect(k, j_5) → K_2,
216. CircleSector(S_1, Z_1, J_2) → f_7
217. CircleSector(S_1, J_2, A_2) → f_5
218. CircleSector(D, K_2, H_2) → h_5
219. Intersect(h, j_5) → L_2,
220. Intersect(h, l_5) → M_2,
221. Intersect(h, i_4) → N_2,
222. CircleSector(C, M_2, L_2) → k_5
223. CircleSector(C, N_2, M_2) → p_5
224. Dilate(D, If[4 < l < 5, 5 - l, 0], S_1) → D'_4
225. Dilate(C, If[4 < l < 5, 5 - l, 0], S_1) → C'_6
226. Vector(D, S_1) → n_5
227. Vector(C, S_1) → q_5
228. Translate(h_5, n_5) → r_5
229. Mirror(r_5, S_1) → s_5
230. Vector(D, D'_4) → t_5
231. Translate(h_5, t_5) → d_6
232. Rotate(d_6, If[4 < l < 5, (((l - 4) * 180))°, 0], D'_4) → e_6
233. Translate(k_5, q_5) → f_6
234. Vector(C, C'_6) → g_6
235. Translate(k_5, g_6) → h_6
236. Dilate(S_1, If[5 < l < 6, 6 - l, 0], N_1) → O_2
237. Dilate(C, If[5 < l < 6, 6 - l, 0], N_1) → C'_7
238. Vector(C, N_1) → k_6
239. Translate(p_5, k_6) → p_6
240. Vector(C, C'_7) → n_6
241. Translate(p_5, n_6) → q_6
242. Vector(S_1, N_1) → s_6
243. Translate(f_5, s_6) → t_6
244. Mirror(t_6, N_1) → d_7
245. Vector(S_1, O_2) → u_7
246. Translate(f_5, u_7) → e_7
247. Rotate(e_7, If[5 < l < 6, (((l - 5) * 180))°, 0], O_2) → g_7
248. Ray(C, S_1) → b_8
249. Polygon(D, C, S_1) → poly5, s_8, d_9, c_8
250. Polygon(S_1, C, N_1) → poly6, n_8, s_9, c_{10}