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Lines of Symmetry by Adam Bevan

Lines of Symmetry by Adam Bevan
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2016-01-10 19:14
Coordinate GeometryTransformationGeometric Construction
This example demonstrates the lines of symmetry in geometric shapes. Key mathematical concepts include symmetry in geometry. It uses GeoGebra commands such as Segment, Line, Mirror, and Intersect to construct the shapes. Suitable for middle school and above students to learn about symmetry.

GeoGebra Commands & Parameters

  1. Segment(E, F) → p
  2. Line(J, K) → b_1
  3. Point(b_1) → L
  4. Point(b_1) → N
  5. Point(b_1) → O
  6. Point(b_1) → Q
  7. Mirror(M, b_1) → M'
  8. Point(b_1) → P
  9. Point(b_1) → R
  10. Segment(P, M) → c_1
  11. Segment(M, R) → f_1
  12. Segment(R, M') → g_1
  13. Segment(M', P) → h_1
  14. Segment(P, R) → i_1
  15. Segment(M, M') → j_1
  16. Intersect(i_1, j_1) → S
  17. Line(P, M') → k_1
  18. Line(M, R) → l_1
  19. Line(R, M') → m_1
  20. Line(M, P) → n_1
  21. Polygon(P, M, R, M') → poly3, p_1, m_2, r_1, m'
  22. Distance(P, M) → distancePM
  23. Distance(M, R) → distanceMR
  24. Distance(R, M') → distanceRM'
  25. Distance(M', P) → distanceM'P
  26. Angle(M', P, M) → ζ
  27. Angle(P, M, R) → η
  28. Angle(M, R, M') → θ
  29. Angle(R, M', P) → ι
  30. Angle(P, S, M') → κ
  31. Distance(M', M) → distanceM'M
  32. Distance(P, R) → distancePR
  33. Segment(T, U) → d_1
  34. Circle(S, Segment[U, T]) → e_1
  35. Point(e_1) → V
  36. Line(V, S) → q_1
  37. Mirror(P, q_1) → P'
  38. Mirror(M, q_1) → M'_1
  39. Mirror(R, q_1) → R'
  40. Mirror(M', q_1) → M''
  41. Polygon(P', M'_1, R', M'') → poly3', p', m'_1, r', m''
  42. Line(W, Z) → s_1
  43. Point(s_1) → B_1
  44. Point(s_1) → C_1
  45. Segment(B_1, C_1) → a_2
  46. Point(s_1) → D_1
  47. Point(s_1) → E_1
  48. Segment(D_1, E_1) → b_2
  49. Point(a_2) → H_1
  50. Line(A_1, F_1) → t_1
  51. Line(G_1, t_1) → c_2
  52. Point(c_2) → I_1
  53. Line(A_1, G_1) → h_2
  54. Line(F_1, I_1) → i_2
  55. Line(A_1, F_1) → j_2
  56. Line(I_1, G_1) → k_2
  57. Distance(G_1, A_1) → distanceG1A1
  58. Distance(A_1, F_1) → distanceA1F1
  59. Distance(F_1, I_1) → distanceF1I1
  60. Distance(I_1, G_1) → distanceI1G1
  61. Angle(I_1, G_1, A_1) → λ
  62. Angle(G_1, A_1, F_1) → μ
  63. Angle(A_1, F_1, I_1) → ν
  64. Angle(F_1, I_1, G_1) → ξ
  65. Segment(A_1, I_1) → l_2
  66. Segment(G_1, F_1) → n_2
  67. Intersect(l_2, n_2) → K_1
  68. Distance(G_1, F_1) → distanceG1F1
  69. Distance(A_1, I_1) → distanceA1I1
  70. Angle(G_1, K_1, I_1) → ο
  71. Polygon(G_1, A_1, F_1, I_1) → poly4, g_2, a_3, f_2, i_3
  72. Segment(J_1, L_1) → d_2
  73. Circle(K_1, Segment[J_1, L_1]) → e_2
  74. Point(e_2) → M_1
  75. Line(K_1, M_1) → p_2
  76. Mirror(G_1, p_2) → N_1
  77. Mirror(A_1, p_2) → O_1
  78. Mirror(F_1, p_2) → P_1
  79. Mirror(I_1, p_2) → Q_1
  80. Polygon(N_1, O_1, P_1, Q_1) → poly4', n_3, o_1, p_3, q_2
  81. Intersect(f_2, g_2) → Z_1
  82. Segment(B_2, C_2) → a_4
  83. Line(I_2, J_2) → d_4
  84. Line(K_2, d_4) → i_4
  85. Line(K_2, I_2) → j_4
  86. Line(J_2, j_4) → k_4
  87. Intersect(i_4, k_4) → L_2
  88. Polygon(K_2, I_2, J_2, L_2) → poly6, k_5, i_5, j_5, l_4
  89. Line(I_2, K_2) → m_4
  90. Line(J_2, L_2) → n_4
  91. Line(I_2, J_2) → p_4
  92. Line(K_2, L_2) → q_4
  93. Segment(K_2, J_2) → r_4
  94. Segment(I_2, L_2) → s_4
  95. Intersect(r_4, s_4) → M_2
  96. Segment(N_2, O_2) → t_4
  97. Circle(M_2, Segment[N_2, O_2]) → c_5
  98. Point(c_5) → P_2
  99. Line(M_2, P_2) → a_5
  100. Mirror(K_2, a_5) → Q_2
  101. Mirror(I_2, a_5) → R_2
  102. Mirror(J_2, a_5) → S_2
  103. Mirror(L_2, a_5) → T_2
  104. Polygon(Q_2, R_2, S_2, T_2) → poly6', q_5, r_5, s_5, t_5
  105. Distance(I_2, K_2) → distanceI2K2
  106. Distance(K_2, L_2) → distanceK2L2
  107. Distance(L_2, J_2) → distanceL2J2
  108. Distance(J_2, I_2) → distanceJ2I2
  109. Distance(I_2, L_2) → distanceI2L2
  110. Distance(K_2, J_2) → distanceK2J2
  111. Angle(J_2, I_2, K_2) → χ
  112. Angle(I_2, K_2, L_2) → ψ
  113. Angle(K_2, L_2, J_2) → ω
  114. Angle(L_2, J_2, I_2) → α_1
  115. Angle(I_2, M_2, J_2) → β_1
  116. Distance(I_2, J_2) → distanceI2J2
  117. Distance(I_2, L_2) → v_1
  118. Distance(K_2, J_2) → w_1
  119. Circle(U_2, V_2) → d_5
  120. Point(d_5) → W_2
  121. Segment(V_2, W_2) → b_5
  122. Mirror(U_2, b_5) → Z_2
  123. Polygon(W_2, U_2, V_2, Z_2) → poly7, w_2, u_2, v_2, z_2
  124. Segment(U_2, Z_2) → e_5
  125. Intersect(b_5, e_5) → A_3
  126. Distance(W_2, V_2) → distanceW2V2
  127. Distance(U_2, Z_2) → distanceU2Z2
  128. Angle(W_2, A_3, Z_2) → γ_1
  129. Angle(Z_2, W_2, U_2) → δ_1
  130. Angle(W_2, U_2, V_2) → ε_1
  131. Angle(U_2, V_2, Z_2) → ζ_1
  132. Angle(V_2, Z_2, W_2) → η_1
  133. Distance(W_2, U_2) → distanceW2U2
  134. Distance(U_2, V_2) → distanceU2V2
  135. Distance(V_2, Z_2) → distanceV2Z2
  136. Distance(Z_2, W_2) → distanceZ2W2
  137. Segment(B_3, C_3) → f_5
  138. Circle(A_3, Segment[B_3, C_3]) → g_5
  139. Point(g_5) → D_3
  140. Line(D_3, A_3) → h_5
  141. Mirror(W_2, h_5) → E_3
  142. Mirror(U_2, h_5) → F_3
  143. Mirror(V_2, h_5) → G_3
  144. Mirror(Z_2, h_5) → H_3
  145. Polygon(E_3, F_3, G_3, H_3) → poly7', e_6, f_6, g_6, h_6
  146. Line(W_2, U_2) → l_5
  147. Line(U_2, V_2) → m_5
  148. Line(V_2, Z_2) → n_5
  149. Line(Z_2, W_2) → p_5
  150. Segment(I_3, J_3) → a_6
  151. OrthogonalLine(I_3, a_6) → b_6
  152. OrthogonalLine(J_3, a_6) → c_6
  153. Point(b_6) → K_3
  154. Line(K_3, b_6) → d_6
  155. Line(K_3, d_6) → i_6
  156. Line(K_3, a_6) → j_6
  157. Intersect(c_6, j_6) → L_3
  158. Polygon(I_3, K_3, L_3, J_3) → poly8, i_7, k_6, l_6, j_7
  159. Distance(I_3, K_3) → distanceI3K3
  160. Distance(K_3, L_3) → distanceK3L3
  161. Distance(L_3, J_3) → distanceL3J3
  162. Distance(J_3, I_3) → distanceJ3I3
  163. Angle(J_3, I_3, K_3) → θ_1
  164. Angle(I_3, K_3, L_3) → ι_1
  165. Angle(K_3, L_3, J_3) → κ_1
  166. Angle(L_3, J_3, I_3) → λ_1
  167. Segment(K_3, J_3) → m_6
  168. Segment(I_3, L_3) → n_6
  169. Intersect(m_6, n_6) → M_3
  170. Line(I_3, K_3) → p_6
  171. Line(K_3, L_3) → q_6
  172. Line(L_3, J_3) → r_6
  173. Line(J_3, I_3) → s_6
  174. Angle(I_3, M_3, J_3) → μ_1
  175. Distance(I_3, L_3) → distanceI3L3
  176. Distance(K_3, J_3) → distanceK3J3
  177. Segment(N_3, O_3) → t_6
  178. Circle(M_3, Segment[N_3, O_3]) → c_7
  179. Point(c_7) → P_3
  180. Line(M_3, P_3) → a_7
  181. Mirror(I_3, a_7) → Q_3
  182. Mirror(K_3, a_7) → R_3
  183. Mirror(L_3, a_7) → S_3
  184. Mirror(J_3, a_7) → T_3
  185. Polygon(Q_3, R_3, S_3, T_3) → poly8', q_7, r_7, s_7, t_7
  186. Segment(A, G) → a
  187. OrthogonalLine(A, a) → b
  188. OrthogonalLine(G, a) → c
  189. Circle(A, Segment[A, G]) → d
  190. Circle(G, Segment[A, G]) → e
  191. Intersect(d, b, 2) → H
  192. Intersect(e, c, 2) → I
  193. Polygon(A, H, I, G) → poly1, a_1, h, i, g_7
  194. Segment(H, G) → l
  195. Segment(I, A) → n
  196. Intersect(l, n) → U_3
  197. Line(H, I) → q
  198. Line(G, A) → r
  199. Line(A, H) → b_7
  200. Line(I, G) → d_7
  201. Angle(G, U_3, I) → α
  202. Angle(G, A, H) → β
  203. Angle(A, H, I) → δ
  204. Angle(H, I, G) → ε
  205. Angle(I, G, A) → ν_1
  206. Distance(A, H) → distanceAH
  207. Distance(H, I) → distanceHI
  208. Distance(I, G) → distanceIG
  209. Distance(G, A) → distanceGA
  210. Distance(A, I) → distanceAI
  211. Distance(H, G) → distanceHG
  212. Segment(B_4, C_4) → m_7
  213. Segment(F_4, G_4) → a_8
  214. Circle(U_3, Segment[F_4, G_4]) → f_8
  215. Point(f_8) → H_4
  216. Line(U_3, H_4) → g_8
  217. Mirror(A, g_8) → A'
  218. Mirror(H, g_8) → H'
  219. Mirror(I, g_8) → I'
  220. Mirror(G, g_8) → G'
  221. Polygon(A', H', I', G') → poly1', a', h', i', g'
  222. Segment(B, C) → f

AI Drawing Prompt Reference

Draw a geometric shape with quadrilateral PMRM' and its axes of symmetry. Start by drawing segment PM, then draw axis b1. Next, draw points L, N, O, Q, P, and R. Use the mirror command to get M', P', M'_1, R', and M''. Finally, draw quadrilateral P'M'_1R'M''.
The prompt above was compiled from the original drawing commands and is for reference only.