Lines of Symmetry in Quadrilaterals

GeoGebra Commands & Parameters

1. Line(D, C) → f
2. Line(B, C) → g
3. Segment(B, C) → j
4. Segment(C, D) → k
5. Line(B, D) → m
6. Segment(E, F) → p
7. Segment(B, D) → t
8. Angle(B, C, D) → γ
9. Distance(B, C) → distanceBC
10. Distance(C, D) → distanceCD
11. Distance(D, B) → distanceDB
12. Line(J, K) → b_1
13. Point(b_1) → L
14. Point(b_1) → N
15. Point(b_1) → O
16. Point(b_1) → Q
17. Mirror(M, b_1) → M'
18. Point(b_1) → P
19. Point(b_1) → R
20. Segment(P, M) → c_1
21. Segment(M, R) → f_1
22. Segment(R, M') → g_1
23. Segment(M', P) → h_1
24. Segment(P, R) → i_1
25. Segment(M, M') → j_1
26. Intersect(i_1, j_1) → S
27. Line(P, M') → k_1
28. Line(M, R) → l_1
29. Line(R, M') → m_1
30. Line(M, P) → n_1
31. Polygon(P, M, R, M') → poly3, p_1, m_2, r_1, m'
32. Distance(P, M) → distancePM
33. Distance(M, R) → distanceMR
34. Distance(R, M') → distanceRM'
35. Distance(M', P) → distanceM'P
36. Angle(M', P, M) → ζ
37. Angle(P, M, R) → η
38. Angle(M, R, M') → θ
39. Angle(R, M', P) → ι
40. Angle(P, S, M') → κ
41. Distance(M', M) → distanceM'M
42. Distance(P, R) → distancePR
43. Segment(T, U) → d_1
44. Circle(S, Segment[U, T]) → e_1
45. Point(e_1) → V
46. Line(V, S) → q_1
47. Mirror(P, q_1) → P'
48. Mirror(M, q_1) → M'_1
49. Mirror(R, q_1) → R'
50. Mirror(M', q_1) → M''
51. Polygon(P', M'_1, R', M'') → poly3', p', m'_1, r', m''
52. Line(W, Z) → s_1
53. Point(s_1) → B_1
54. Point(s_1) → C_1
55. Segment(B_1, C_1) → a_2
56. Point(s_1) → D_1
57. Point(s_1) → E_1
58. Segment(D_1, E_1) → b_2
59. Point(a_2) → H_1
60. Line(A_1, F_1) → t_1
61. Line(G_1, t_1) → c_2
62. Point(c_2) → I_1
63. Line(A_1, G_1) → h_2
64. Line(F_1, I_1) → i_2
65. Line(A_1, F_1) → j_2
66. Line(I_1, G_1) → k_2
67. Distance(G_1, A_1) → distanceG1A1
68. Distance(A_1, F_1) → distanceA1F1
69. Distance(F_1, I_1) → distanceF1I1
70. Distance(I_1, G_1) → distanceI1G1
71. Angle(I_1, G_1, A_1) → λ
72. Angle(G_1, A_1, F_1) → μ
73. Angle(A_1, F_1, I_1) → ν
74. Angle(F_1, I_1, G_1) → ξ
75. Segment(A_1, I_1) → l_2
76. Segment(G_1, F_1) → n_2
77. Intersect(l_2, n_2) → K_1
78. Distance(G_1, F_1) → distanceG1F1
79. Distance(A_1, I_1) → distanceA1I1
80. Angle(G_1, K_1, I_1) → ο
81. Polygon(G_1, A_1, F_1, I_1) → poly4, g_2, a_3, f_2, i_3
82. Segment(J_1, L_1) → d_2
83. Circle(K_1, Segment[J_1, L_1]) → e_2
84. Point(e_2) → M_1
85. Line(K_1, M_1) → p_2
86. Mirror(G_1, p_2) → N_1
87. Mirror(A_1, p_2) → O_1
88. Mirror(F_1, p_2) → P_1
89. Mirror(I_1, p_2) → Q_1
90. Polygon(N_1, O_1, P_1, Q_1) → poly4', n_3, o_1, p_3, q_2
91. Line(R_1, S_1) → r_2
92. Line(T_1, r_2) → s_2
93. Segment(R_1, T_1) → t_2
94. Circle(S_1, Segment[R_1, S_1]) → c_3
95. Circle(S_1, Segment[R_1, T_1]) → d_3
96. Circle(R_1, Segment[T_1, S_1]) → e_3
97. Intersect(d_3, e_3, 2) → U_1
98. Segment(T_1, U_1) → b_3
99. Segment(U_1, S_1) → f_3
100. Segment(S_1, R_1) → g_3
101. Intersect(t_2, f_3) → V_1
102. Intersect(b_3, g_3) → W_1
103. Distance(U_1, V_1) → distanceU1V1
104. Distance(U_1, W_1) → distanceU1W1
105. Intersect(f_2, g_2) → Z_1
106. Polygon(R_1, T_1, U_1, S_1) → poly5, r_3, t_3, u_1, s_3
107. Line(R_1, T_1) → h_3
108. Line(S_1, U_1) → j_3
109. Line(T_1, U_1) → k_3
110. Line(R_1, S_1) → l_3
111. Segment(T_1, S_1) → m_3
112. Segment(R_1, U_1) → q_3
113. Intersect(m_3, q_3) → A_2
114. Segment(B_2, C_2) → a_4
115. Circle(A_2, Segment[B_2, C_2]) → c_4
116. Point(c_4) → D_2
117. Line(A_2, D_2) → b_4
118. Mirror(R_1, b_4) → E_2
119. Mirror(T_1, b_4) → F_2
120. Mirror(U_1, b_4) → G_2
121. Mirror(S_1, b_4) → H_2
122. Polygon(E_2, F_2, G_2, H_2) → poly5', e_4, f_4, g_4, h_4
123. Distance(R_1, T_1) → distanceR1T1
124. Distance(T_1, U_1) → distanceT1U1
125. Distance(U_1, S_1) → distanceU1S1
126. Distance(S_1, R_1) → distanceS1R1
127. Distance(R_1, U_1) → distanceR1U1
128. Distance(T_1, S_1) → distanceT1S1
129. Angle(R_1, A_2, S_1) → ρ
130. Angle(S_1, R_1, T_1) → σ
131. Angle(R_1, T_1, U_1) → τ
132. Angle(T_1, U_1, S_1) → υ
133. Angle(U_1, S_1, R_1) → ϕ
134. Line(I_2, J_2) → d_4
135. Line(K_2, d_4) → i_4
136. Line(K_2, I_2) → j_4
137. Line(J_2, j_4) → k_4
138. Intersect(i_4, k_4) → L_2
139. Polygon(K_2, I_2, J_2, L_2) → poly6, k_5, i_5, j_5, l_4
140. Line(I_2, K_2) → m_4
141. Line(J_2, L_2) → n_4
142. Line(I_2, J_2) → p_4
143. Line(K_2, L_2) → q_4
144. Segment(K_2, J_2) → r_4
145. Segment(I_2, L_2) → s_4
146. Intersect(r_4, s_4) → M_2
147. Segment(N_2, O_2) → t_4
148. Circle(M_2, Segment[N_2, O_2]) → c_5
149. Point(c_5) → P_2
150. Line(M_2, P_2) → a_5
151. Mirror(K_2, a_5) → Q_2
152. Mirror(I_2, a_5) → R_2
153. Mirror(J_2, a_5) → S_2
154. Mirror(L_2, a_5) → T_2
155. Polygon(Q_2, R_2, S_2, T_2) → poly6', q_5, r_5, s_5, t_5
156. Distance(I_2, K_2) → distanceI2K2
157. Distance(K_2, L_2) → distanceK2L2
158. Distance(L_2, J_2) → distanceL2J2
159. Distance(J_2, I_2) → distanceJ2I2
160. Distance(I_2, L_2) → distanceI2L2
161. Distance(K_2, J_2) → distanceK2J2
162. Angle(J_2, I_2, K_2) → χ
163. Angle(I_2, K_2, L_2) → ψ
164. Angle(K_2, L_2, J_2) → ω
165. Angle(L_2, J_2, I_2) → α_1
166. Angle(I_2, M_2, J_2) → β_1
167. Distance(I_2, J_2) → distanceI2J2
168. Distance(I_2, L_2) → v_1
169. Distance(K_2, J_2) → w_1
170. Circle(U_2, V_2) → d_5
171. Point(d_5) → W_2
172. Segment(V_2, W_2) → b_5
173. Mirror(U_2, b_5) → Z_2
174. Polygon(W_2, U_2, V_2, Z_2) → poly7, w_2, u_2, v_2, z_2
175. Segment(U_2, Z_2) → e_5
176. Intersect(b_5, e_5) → A_3
177. Distance(W_2, V_2) → distanceW2V2
178. Distance(U_2, Z_2) → distanceU2Z2
179. Angle(W_2, A_3, Z_2) → γ_1
180. Angle(Z_2, W_2, U_2) → δ_1
181. Angle(W_2, U_2, V_2) → ε_1
182. Angle(U_2, V_2, Z_2) → ζ_1
183. Angle(V_2, Z_2, W_2) → η_1
184. Distance(W_2, U_2) → distanceW2U2
185. Distance(U_2, V_2) → distanceU2V2
186. Distance(V_2, Z_2) → distanceV2Z2
187. Distance(Z_2, W_2) → distanceZ2W2
188. Segment(B_3, C_3) → f_5
189. Circle(A_3, Segment[B_3, C_3]) → g_5
190. Point(g_5) → D_3
191. Line(D_3, A_3) → h_5
192. Mirror(W_2, h_5) → E_3
193. Mirror(U_2, h_5) → F_3
194. Mirror(V_2, h_5) → G_3
195. Mirror(Z_2, h_5) → H_3
196. Polygon(E_3, F_3, G_3, H_3) → poly7', e_6, f_6, g_6, h_6
197. Line(W_2, U_2) → l_5
198. Line(U_2, V_2) → m_5
199. Line(V_2, Z_2) → n_5
200. Line(Z_2, W_2) → p_5
201. Segment(I_3, J_3) → a_6
202. OrthogonalLine(I_3, a_6) → b_6
203. OrthogonalLine(J_3, a_6) → c_6
204. Point(b_6) → K_3
205. Line(K_3, b_6) → d_6
206. Line(K_3, d_6) → i_6
207. Line(K_3, a_6) → j_6
208. Intersect(c_6, j_6) → L_3
209. Polygon(I_3, K_3, L_3, J_3) → poly8, i_7, k_6, l_6, j_7
210. Distance(I_3, K_3) → distanceI3K3
211. Distance(K_3, L_3) → distanceK3L3
212. Distance(L_3, J_3) → distanceL3J3
213. Distance(J_3, I_3) → distanceJ3I3
214. Angle(J_3, I_3, K_3) → θ_1
215. Angle(I_3, K_3, L_3) → ι_1
216. Angle(K_3, L_3, J_3) → κ_1
217. Angle(L_3, J_3, I_3) → λ_1
218. Segment(K_3, J_3) → m_6
219. Segment(I_3, L_3) → n_6
220. Intersect(m_6, n_6) → M_3
221. Line(I_3, K_3) → p_6
222. Line(K_3, L_3) → q_6
223. Line(L_3, J_3) → r_6
224. Line(J_3, I_3) → s_6
225. Angle(I_3, M_3, J_3) → μ_1
226. Distance(I_3, L_3) → distanceI3L3
227. Distance(K_3, J_3) → distanceK3J3
228. Segment(N_3, O_3) → t_6
229. Circle(M_3, Segment[N_3, O_3]) → c_7
230. Point(c_7) → P_3
231. Line(M_3, P_3) → a_7
232. Mirror(I_3, a_7) → Q_3
233. Mirror(K_3, a_7) → R_3
234. Mirror(L_3, a_7) → S_3
235. Mirror(J_3, a_7) → T_3
236. Polygon(Q_3, R_3, S_3, T_3) → poly8', q_7, r_7, s_7, t_7
237. Segment(A, G) → a
238. OrthogonalLine(A, a) → b
239. OrthogonalLine(G, a) → c
240. Circle(A, Segment[A, G]) → d
241. Circle(G, Segment[A, G]) → e
242. Intersect(d, b, 2) → H
243. Intersect(e, c, 2) → I
244. Polygon(A, H, I, G) → poly1, a_1, h, i, g_7
245. Segment(H, G) → l
246. Segment(I, A) → n
247. Intersect(l, n) → U_3
248. Line(H, I) → q
249. Line(G, A) → r
250. Line(A, H) → b_7
251. Line(I, G) → d_7
252. Angle(G, U_3, I) → α
253. Angle(G, A, H) → β
254. Angle(A, H, I) → δ
255. Angle(H, I, G) → ε
256. Angle(I, G, A) → ν_1
257. Distance(A, H) → distanceAH
258. Distance(H, I) → distanceHI
259. Distance(I, G) → distanceIG
260. Distance(G, A) → distanceGA
261. Distance(A, I) → distanceAI
262. Distance(H, G) → distanceHG
263. Segment(B, V_3) → e_7
264. Segment(V_3, D) → f_7
265. Polygon(V_3, B, C, D) → poly2, v_3, b_8, c_8, d_8
266. Line(B, V_3) → h_7
267. Line(V_3, D) → k_7
268. Segment(C, V_3) → l_7
269. Intersect(t, l_7) → W_3
270. Intersect(c_8, v_3) → Z_3
271. Intersect(d_8, b_8) → A_4
272. Segment(B_4, C_4) → m_7
273. Circle(W_3, Segment[B_4, C_4]) → p_7
274. Point(p_7) → D_4
275. Line(W_3, D_4) → n_7
276. Mirror(V_3, n_7) → E_4
277. Mirror(B, n_7) → B'
278. Mirror(C, n_7) → C'
279. Mirror(D, n_7) → D'
280. Polygon(E_4, B', C', D') → poly2', e_8, b', c', d'
281. Mirror(B', b') → B''
282. Mirror(C', b') → C''
283. Distance(V_3, B) → distanceV3B
284. Distance(B, C) → z_1
285. Distance(C, D) → o_2
286. Distance(D, V_3) → distanceDV3
287. Distance(V_3, C) → distanceV3C
288. Distance(B, D) → distanceBD
289. Angle(D, V_3, B) → ξ_1
290. Angle(V_3, B, C) → ο_1
291. Angle(B, C, D) → ρ_1
292. Angle(C, D, V_3) → σ_1
293. Angle(V_3, W_3, D) → τ_1
294. Segment(F_4, G_4) → a_8
295. Circle(U_3, Segment[F_4, G_4]) → f_8
296. Point(f_8) → H_4
297. Line(U_3, H_4) → g_8
298. Mirror(A, g_8) → A'
299. Mirror(H, g_8) → H'
300. Mirror(I, g_8) → I'
301. Mirror(G, g_8) → G'
302. Polygon(A', H', I', G') → poly1', a', h', i', g'