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Oscar's Parallelogram, Rhombus, Rectangle, Square, Kite, Trapezoid

Oscar's Parallelogram, Rhombus, Rectangle, Square, Kite, Trapezoid
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2016-03-17 22:43
PolygonAngleGeometric Construction
This example demonstrates Oscar's parallelogram, rhombus, rectangle, square, kite, and trapezoid. It involves key mathematical concepts such as geometric construction, angles, and distances. Using GeoGebra commands like Line, Point, Segment, Intersect, Angle, Circle, etc., these shapes can be constructed. Suitable for middle and high school students learning geometric construction and related concepts.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(C, a) → b
  3. Point(b) → D
  4. Segment(A, D) → c
  5. Line(B, c) → d
  6. Intersect(d, b) → E
  7. Segment(B, E) → e
  8. Segment(A, B) → f
  9. Segment(E, D) → g
  10. Angle(A, B, E) → α
  11. Angle(B, E, D) → β
  12. Angle(E, D, A) → γ
  13. Angle(D, A, B) → δ
  14. Segment(B, D) → h
  15. Segment(A, E) → i
  16. Intersect(i, h) → F
  17. Angle(A, F, D) → ε
  18. Angle(D, F, E) → ζ
  19. Angle(E, F, B) → η
  20. Angle(B, F, A) → θ
  21. Circle(G, H) → k
  22. Point(k) → I
  23. Circle(I, G) → p
  24. Circle(H, G) → q
  25. Intersect(p, q, 2) → J
  26. Segment(I, J) → j
  27. Segment(J, H) → l
  28. Segment(H, G) → m
  29. Segment(G, I) → n
  30. Segment(J, G) → r
  31. Segment(I, H) → s
  32. Intersect(r, s) → K
  33. Segment(I, K) → t
  34. Segment(K, H) → a_1
  35. Segment(J, K) → b_1
  36. Segment(K, G) → c_1
  37. Angle(H, K, J) → ι
  38. Angle(G, K, H) → κ
  39. Angle(I, K, G) → λ
  40. Angle(J, K, I) → μ
  41. Segment(L, M) → d_1
  42. Line(N, d_1) → e_1
  43. OrthogonalLine(L, e_1) → f_1
  44. Intersect(f_1, e_1) → O
  45. OrthogonalLine(M, e_1) → g_1
  46. Intersect(e_1, g_1) → P
  47. Segment(L, O) → h_1
  48. Segment(O, P) → i_1
  49. Segment(P, M) → j_1
  50. Angle(O, L, M) → ν
  51. Angle(L, M, P) → ξ
  52. Angle(M, P, O) → ο
  53. Angle(P, O, L) → ρ
  54. Segment(M, O) → k_1
  55. Segment(L, P) → l_1
  56. Intersect(l_1, k_1) → Q
  57. Segment(M, Q) → m_1
  58. Segment(Q, L) → n_1
  59. Segment(Q, O) → p_1
  60. Segment(Q, P) → q_1
  61. Angle(L, Q, O) → σ
  62. Angle(O, Q, P) → τ
  63. Angle(P, Q, M) → υ
  64. Angle(M, Q, L) → ϕ
  65. Segment(R, S) → r_1
  66. OrthogonalLine(R, r_1) → s_1
  67. OrthogonalLine(S, r_1) → t_1
  68. Circle(R, S) → c_2
  69. Intersect(c_2, s_1, 2) → T
  70. OrthogonalLine(T, s_1) → a_2
  71. Intersect(t_1, a_2) → U
  72. Segment(R, T) → b_2
  73. Segment(T, U) → d_2
  74. Segment(U, S) → e_2
  75. Angle(R, T, U) → χ
  76. Angle(T, U, S) → ψ
  77. Angle(U, S, R) → ω
  78. Angle(S, R, T) → α_1
  79. Segment(V, W) → f_2
  80. Point(f_2) → Z
  81. OrthogonalLine(Z, f_2) → g_2
  82. Point(g_2) → A_1
  83. Circle(Z, A_1) → h_2
  84. Intersect(h_2, g_2, 2) → B_1
  85. Point(h_2) → C_1
  86. Segment(V, A_1) → i_2
  87. Segment(V, B_1) → j_2
  88. Segment(B_1, W) → k_2
  89. Segment(W, A_1) → l_2
  90. Segment(D_1, E_1) → m_2
  91. Point(m_2) → F_1
  92. OrthogonalLine(F_1, m_2) → n_2
  93. Point(n_2) → G_1
  94. Circle(F_1, G_1) → p_2
  95. Intersect(p_2, n_2, 2) → H_1
  96. Segment(D_1, G_1) → q_2
  97. Segment(D_1, H_1) → r_2
  98. Segment(H_1, E_1) → s_2
  99. Segment(E_1, G_1) → t_2
  100. Segment(I_1, J_1) → a_3
  101. OrthogonalLine(I_1, a_3) → b_3
  102. OrthogonalLine(J_1, a_3) → c_3
  103. Point(b_3) → K_1
  104. OrthogonalLine(K_1, b_3) → d_3
  105. Intersect(c_3, d_3) → L_1
  106. Segment(K_1, L_1) → e_3
  107. Point(e_3) → M_1
  108. Segment(I_1, M_1) → f_3
  109. Circle(J_1, f) → g_3
  110. Intersect(g_3, e_3, 1) → N_1
  111. Segment(J_1, N_1) → h_3
  112. Segment(M_1, N_1) → i_3
  113. Segment(O_1, P_1) → j_3
  114. OrthogonalLine(O_1, j_3) → k_3
  115. OrthogonalLine(P_1, j_3) → l_3
  116. Point(k_3) → Q_1
  117. OrthogonalLine(Q_1, k_3) → m_3
  118. Intersect(l_3, m_3) → R_1
  119. Segment(Q_1, R_1) → n_3
  120. Point(n_3) → S_1
  121. Segment(O_1, S_1) → p_3
  122. Circle(P_1, 3.08) → q_3
  123. Circle(P_1, 3.124410319967215) → r_3
  124. Point(r_3) → T_1
  125. Circle(P_1, 6.95) → s_3
  126. Circle(P_1, 6.919440774045372) → t_3
  127. Point(s_3) → U_1
  128. Circle(P_1, 6.962364924165079) → c_4
  129. Point(Circle[V_1, 9]) → W_1
  130. Segment(V_1, W_1) → a_4
  131. Line(Z_1, a_4) → b_4
  132. Point(b_4) → A_2
  133. Segment(V_1, A_2) → d_4
  134. Circle(W_1, 6.83) → e_4
  135. Intersect(e_4, b_4, 1) → B_2
  136. Segment(W_1, B_2) → f_4
  137. Segment(A_2, B_2) → g_4
  138. Segment(C_2, D_2) → h_4
  139. OrthogonalLine(C_2, h_4) → i_4
  140. OrthogonalLine(D_2, h_4) → j_4
  141. Point(i_4) → E_2
  142. OrthogonalLine(E_2, i_4) → k_4
  143. Intersect(j_4, k_4) → F_2
  144. Segment(E_2, F_2) → l_4
  145. Point(l_4) → G_2
  146. Point(l_4) → H_2
  147. Point(l_4) → J_2
  148. Segment(G_2, J_2) → m_4
  149. Segment(C_2, G_2) → n_4
  150. Segment(D_2, J_2) → p_4
  151. Segment(D_1, E_1) → q_4
  152. Segment(G_1, H_1) → r_4
  153. Segment(D_1, F_1) → s_4
  154. Segment(F_1, E_1) → t_4
  155. Segment(G_1, F_1) → a_5
  156. Segment(F_1, H_1) → b_5
  157. Angle(G_1, F_1, E_1) → β_1
  158. Angle(E_1, F_1, G_1) → γ_1
  159. Angle(H_1, F_1, E_1) → δ_1
  160. Angle(D_1, F_1, H_1) → ε_1
  161. Angle(G_1, F_1, D_1) → ζ_1
  162. Distance(q_2, t_2) → o
  163. Distance(U, d_2) → distanceUd2
  164. Segment(K_2, L_2) → c_5
  165. OrthogonalLine(M_2, c_5) → d_5
  166. OrthogonalLine(K_2, c_5) → e_5
  167. OrthogonalLine(L_2, c_5) → f_5
  168. Point(e_5) → N_2
  169. OrthogonalLine(O_2, e_5) → g_5
  170. OrthogonalLine(N_2, e_5) → h_5
  171. Intersect(f_5, h_5) → P_2
  172. Segment(N_2, P_2) → i_5
  173. Point(i_5) → Q_2
  174. Point(i_5) → R_2
  175. Point(i_5) → S_2
  176. Segment(Q_2, K_2) → j_5
  177. Segment(Q_2, R_2) → k_5
  178. Segment(R_2, L_2) → l_5
  179. Angle(K_2, Q_2, R_2) → η_1
  180. Angle(Q_2, R_2, L_2) → θ_1
  181. Angle(R_2, L_2, K_2) → ι_1
  182. Angle(L_2, K_2, Q_2) → κ_1
  183. Segment(T_2, U_2) → m_5
  184. OrthogonalLine(T_2, m_5) → n_5
  185. OrthogonalLine(U_2, m_5) → p_5
  186. Point(n_5) → V_2
  187. OrthogonalLine(V_2, p_5) → q_5
  188. Intersect(p_5, q_5) → W_2
  189. Segment(R_2, Z_2) → r_5
  190. Point(r_5) → A_3
  191. Segment(A_3, B_3) → s_5
  192. Segment(V_2, W_2) → t_5
  193. Point(t_5) → D_3
  194. Segment(D_3, T_2) → a_6
  195. Circle(U_2, 3.07) → c_6
  196. Intersect(c_6, t_5, 1) → E_3
  197. Segment(E_3, U_2) → b_6
  198. Segment(D_3, E_3) → d_6
  199. Circle(U_2, 3.07) → e_6
  200. Segment(E_3, U_2) → f_6
  201. Segment(F_3, G_3) → g_6
  202. OrthogonalLine(F_3, g_6) → h_6
  203. OrthogonalLine(G_3, g_6) → i_6
  204. Point(h_6) → H_3
  205. OrthogonalLine(H_3, h_6) → j_6
  206. Intersect(i_6, j_6) → I_3
  207. Segment(H_3, I_3) → k_6
  208. Point(k_6) → J_3
  209. Segment(F_3, J_3) → l_6
  210. Circle(G_3, 3.76) → p_6
  211. Intersect(p_6, k_6, 1) → K_3
  212. Segment(G_3, K_3) → m_6
  213. Segment(J_3, K_3) → n_6
  214. Angle(F_3, J_3, K_3) → λ_1
  215. Angle(J_3, K_3, G_3) → μ_1
  216. Angle(K_3, G_3, F_3) → ν_1
  217. Angle(G_3, F_3, J_3) → ξ_1
  218. Point(Circle[L_3, 9]) → M_3
  219. Segment(L_3, M_3) → q_6
  220. Line(N_3, q_6) → r_6
  221. Point(r_6) → O_3
  222. Segment(L_3, O_3) → s_6
  223. Circle(M_3, 6.83) → t_6
  224. Intersect(t_6, r_6, 1) → P_3
  225. Segment(M_3, P_3) → a_7
  226. Segment(O_3, P_3) → b_7
  227. Segment(Q_3, R_3) → c_7
  228. OrthogonalLine(Q_3, c_7) → d_7
  229. OrthogonalLine(R_3, c_7) → e_7
  230. Point(d_7) → S_3
  231. OrthogonalLine(S_3, d_7) → f_7
  232. Intersect(e_7, f_7) → T_3
  233. Segment(S_3, T_3) → g_7
  234. Point(g_7) → U_3
  235. Segment(Q_3, U_3) → h_7
  236. Circle(R_3, 3.75) → k_7
  237. Intersect(k_7, g_7, 1) → V_3
  238. Segment(R_3, V_3) → i_7
  239. Segment(U_3, V_3) → j_7
  240. Angle(Q_3, U_3, V_3) → ο_1
  241. Angle(U_3, V_3, R_3) → ρ_1
  242. Angle(V_3, R_3, Q_3) → σ_1
  243. Angle(R_3, Q_3, U_3) → τ_1

AI Drawing Prompt Reference

Draw a parallelogram first, then construct a rhombus, rectangle, square, kite, and trapezoid based on it. Start by drawing two intersecting lines AB and BC, then draw a line parallel to AB through point B, intersecting BC at point D, and connect AD and BD to form parallelogram ABCD. Next, draw a circle with center D and radius DA, intersecting AB at point E, and connect BE to form rhombus ABED. Then, draw a circle with center E and radius EA, intersecting BD at point F, and connect EF to form rectangle ABEF. After that, draw a circle with center F and radius FA, intersecting BE at point G, and connect FG to form square ABEF. Then, draw a circle with center G and radius GA, intersecting EF at point H, and connect GH to form kite ABGH. Finally, draw a circle with center H and radius HA, intersecting FG at point I, and connect HI to form trapezoid ABHI.
The prompt above was compiled from the original drawing commands and is for reference only.