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Poorly Drawn Triangles Example

Poorly Drawn Triangles Example
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2021-10-15 19:24
TriangleTrigonometryIntegralGeometric Construction
This example demonstrates the construction of a triangle with specific properties using GeoGebra. It involves core mathematical concepts such as triangles, angles, polygon construction, and integral calculus. The construction utilizes commands like Segment, Intersect, Circle, Angle, Midpoint, Polygon, and InteriorAngles. It is suitable for high school and above students to understand geometric constructions and the application of related mathematical concepts.

GeoGebra Commands & Parameters

  1. Segment(A, D) → a
  2. Segment(B, C) → b
  3. Segment(A, B) → c
  4. Segment(D, C) → d
  5. Segment(A, D) → f
  6. Segment(D, C) → g
  7. Segment(C, B) → h
  8. Segment(B, A) → i
  9. Segment(A, D) → j
  10. Segment(C, B) → l
  11. Segment(B, A) → m
  12. Segment(C, D) → k
  13. Segment(B, A) → n
  14. Segment(A, D) → p
  15. Segment(D, C) → q
  16. Segment(C, B) → r
  17. Segment(B, D) → t
  18. Segment(A, C) → a_1
  19. Intersect(t, a_1) → E_{1}
  20. Segment(A, E_{1}) → b_1
  21. Segment(E_{1}, C) → c_1
  22. Segment(B, E_{1}) → d_1
  23. Segment(E_{1}, D) → e_1
  24. Segment(D, C) → h_1
  25. Segment(A, B) → i_1
  26. Circle(A, 1.5) → k_1
  27. Circle(B, 1.5) → p_1
  28. Segment(A, D) → m_1
  29. Segment(B, C) → n_1
  30. Segment(C, D) → q_1
  31. Segment(B, A) → r_1
  32. Segment(A, C) → s_1
  33. Segment(B, D) → t_1
  34. Segment(A, D) → a_2
  35. Segment(A, B) → b_2
  36. Segment(B, C) → c_2
  37. Segment(C, D) → d_2
  38. Segment(A, B) → e_2
  39. Segment(B, C) → f_2
  40. Segment(C, D) → g_2
  41. Segment(D, A) → h_2
  42. Segment(B, D) → i_2
  43. Angle(A, D, B) → α
  44. Angle(C, B, D) → β
  45. Segment(A, D) → j_2
  46. Segment(D, C) → k_2
  47. Segment(A, B) → l_2
  48. Segment(B, C) → m_2
  49. Segment(D, B) → n_2
  50. Segment(A, C) → p_2
  51. Intersect(n_2, p_2) → H
  52. Angle(D, H, A) → γ
  53. Angle(C, H, D) → δ
  54. Segment(A, D) → q_2
  55. Segment(D, C) → r_2
  56. Segment(C, B) → s_2
  57. Segment(B, A) → t_2
  58. Segment(A, C) → a_3
  59. Segment(B, D) → b_3
  60. Intersect(a_3, b_3) → I
  61. Segment(A, I) → c_3
  62. Segment(I, D) → d_3
  63. Segment(I, C) → e_3
  64. Segment(B, I) → f_3
  65. Segment(A, D) → g_3
  66. Segment(D, C) → h_3
  67. Segment(C, B) → i_3
  68. Segment(B, A) → j_3
  69. Angle(B, A, D) → ε
  70. Angle(D, C, B) → ζ
  71. Angle(C, B, A) → η
  72. Angle(A, D, C) → θ
  73. Segment(A, D) → k_3
  74. Segment(B, C) → l_3
  75. Segment(C, D) → m_3
  76. Segment(B, A) → n_3
  77. Segment(A, C) → p_3
  78. Angle(C, A, D) → ι
  79. Angle(B, A, C) → κ
  80. Angle(A, C, B) → λ
  81. Segment(A, D) → q_3
  82. Segment(D, C) → r_3
  83. Segment(C, B) → s_3
  84. Segment(B, A) → t_3
  85. Segment(B, D) → a_4
  86. Angle(A, D, B) → ν
  87. Angle(B, D, C) → ξ
  88. Angle(C, B, D) → ο
  89. Angle(D, B, A) → ρ
  90. Segment(A, D) → b_4
  91. Segment(D, C) → c_4
  92. Segment(C, B) → d_4
  93. Segment(B, A) → e_4
  94. Angle(A, D, C) → σ
  95. Angle(D, C, B) → τ
  96. Angle(C, B, A) → υ
  97. Angle(B, A, D) → φ
  98. Segment(A, D) → f_4
  99. Segment(B, C) → g_4
  100. Segment(A, B) → h_4
  101. Segment(D, C) → i_4
  102. Segment(A, C) → j_4
  103. Segment(B, D) → k_4
  104. Segment(A, B) → l_4
  105. Segment(D, C) → m_4
  106. Segment(A, D) → n_4
  107. Segment(B, C) → p_4
  108. Segment(B, D) → q_4
  109. Segment(A, C) → r_4
  110. Intersect(q_4, r_4) → J
  111. Angle(A, J, D) → χ
  112. Angle(A, J, B) → ψ
  113. Segment(A, D) → s_4
  114. Segment(B, C) → t_4
  115. Segment(D, C) → a_5
  116. Segment(A, B) → b_5
  117. Segment(A, C) → c_5
  118. Angle(B, A, C) → ω
  119. Angle(D, C, A) → α_1
  120. Segment(B, D) → d_5
  121. Intersect(c_5, d_5) → K
  122. Angle(B, K, C) → β_1
  123. Segment(A, D) → e_5
  124. Segment(D, C) → f_5
  125. Segment(C, B) → g_5
  126. Segment(B, A) → h_5
  127. Segment(A, C) → i_5
  128. Segment(B, D) → j_5
  129. Intersect(i_5, j_5) → L
  130. Segment(A, L) → k_5
  131. Segment(L, B) → l_5
  132. Segment(L, D) → m_5
  133. Segment(L, C) → n_5
  134. Angle(B, L, C) → γ_1
  135. Angle(C, L, D) → δ_1
  136. Segment(A, D) → p_5
  137. Segment(D, C) → q_5
  138. Segment(A, B) → r_5
  139. Segment(B, C) → s_5
  140. Angle(A, D, C) → ε_1
  141. Angle(D, C, B) → ζ_1
  142. Segment(A, D) → t_5
  143. Segment(D, C) → a_6
  144. Segment(C, B) → b_6
  145. Segment(B, A) → c_6
  146. Segment(A, C) → d_6
  147. Segment(B, D) → e_6
  148. Intersect(d_6, e_6) → M
  149. Segment(A, M) → f_6
  150. Segment(M, C) → g_6
  151. Angle(D, M, A) → η_1
  152. Angle(D, M, C) → θ_1
  153. Segment(A, D) → h_6
  154. Segment(B, C) → i_6
  155. Segment(C, D) → j_6
  156. Segment(B, A) → k_6
  157. Angle(B, A, D) → ι_1
  158. Angle(D, C, B) → κ_1
  159. Segment(A, D) → l_6
  160. Segment(D, C) → m_6
  161. Segment(C, B) → n_6
  162. Segment(B, A) → p_6
  163. Angle(D, A, B) → λ_1
  164. Angle(D, C, B) → μ_1
  165. Segment(A, D) → q_6
  166. Segment(D, C) → r_6
  167. Segment(C, B) → s_6
  168. Segment(B, A) → t_6
  169. Segment(B, D) → a_7
  170. Angle(D, B, A) → ν_1
  171. Angle(C, B, D) → ξ_1
  172. Segment(A, D) → b_7
  173. Segment(D, C) → c_7
  174. Segment(C, B) → d_7
  175. Segment(B, A) → e_7
  176. Segment(A, C) → f_7
  177. Angle(D, C, A) → ο_1
  178. Angle(A, C, B) → ρ_1
  179. Segment(A, D) → g_7
  180. Segment(B, C) → h_7
  181. Segment(D, C) → i_7
  182. Segment(A, B) → j_7
  183. Segment(B, D) → k_7
  184. Angle(A, D, B) → σ_1
  185. Angle(B, D, C) → τ_1
  186. Angle(B, A, D) → υ_1
  187. Angle(D, C, B) → φ_1
  188. Segment(A, C) → l_7
  189. Angle(B, A, C) → ϕ
  190. Angle(D, C, A) → ϕ_1
  191. Segment(B, D) → m_7
  192. Segment(A, C) → n_7
  193. Segment(D, B) → p_7
  194. Intersect(n_7, p_7) → E
  195. Segment(B, E) → q_7
  196. Segment(E, D) → r_7
  197. Segment(A, E) → s_7
  198. Segment(E, C) → t_7
  199. Segment(A, C) → f_8
  200. Angle(B, A, C) → χ_1
  201. Angle(A, D, C) → ψ_1
  202. Angle(I, B, A) → ω_1
  203. Angle(D, C, I) → α_2
  204. Intersect(n_2, p_2) → O
  205. Segment(A, O) → g_8
  206. Segment(O, C) → h_8
  207. Segment(A, C) → i_8
  208. Segment(D, B) → j_8
  209. Intersect(i_8, j_8) → F
  210. Segment(B, F) → f_1
  211. Segment(F, D) → g_1
  212. Segment(A, D) → l_1
  213. Segment(D, C) → k_8
  214. Segment(A, C) → j_1
  215. Angle(A, D, C) → μ
  216. Segment(A, C) → l_8
  217. Angle(C, B, D) → β_2
  218. Angle(D, B, A) → γ_2
  219. Segment(A, D) → m_8
  220. Segment(A, C) → n_8
  221. Segment(B, C) → p_8
  222. Angle(C, A, D) → δ_2
  223. Angle(C, B, A) → ε_2
  224. Angle(D, C, A) → ζ_2
  225. Angle(A, C, B) → η_2
  226. Angle(M, A, D) → θ_2
  227. Angle(M, C, B) → ι_2
  228. Segment(B, D) → q_8
  229. Angle(A, D, B) → κ_2
  230. Angle(B, D, C) → λ_2
  231. Segment(B, D) → r_8
  232. Segment(A, D) → s_8
  233. Segment(B, C) → t_8
  234. Segment(A, C) → a_8
  235. Segment(D, B) → b_8
  236. Intersect(a_8, b_8) → G
  237. Segment(D, G) → c_8
  238. Segment(G, B) → d_8
  239. Segment(B, A) → e_8
  240. Segment(C, D) → f_9
  241. Segment(A, D) → g_9
  242. Segment(B, C) → h_9
  243. Segment(B, D) → i_9
  244. Segment(A, D) → j_9
  245. Segment(B, C) → k_9
  246. Segment(A, C) → l_9
  247. Segment(B, D) → m_9
  248. Intersect(l_9, m_9) → P
  249. Midpoint(j_9) → Q
  250. Midpoint(k_9) → R
  251. Segment(A, Q) → n_9
  252. Segment(Q, D) → p_9
  253. Segment(B, R) → q_9
  254. Segment(R, C) → r_9
  255. Segment(A, D) → s_9
  256. Segment(B, C) → t_9
  257. Segment(B, D) → a_9
  258. Segment(A, C) → b_9
  259. Intersect(a_9, b_9) → S
  260. Segment(B, A) → c_9
  261. Segment(C, D) → d_9
  262. Segment(A, D) → e_9
  263. Segment(B, C) → f_{10}
  264. Segment(B, D) → g_{10}
  265. Midpoint(A, C) → T
  266. Midpoint(D, B) → U
  267. Segment(A, B) → h_{10}
  268. Segment(B, U) → i_{10}
  269. Segment(U, A) → j_{10}
  270. Segment(T, D) → k_{10}
  271. Segment(D, C) → l_{10}
  272. Segment(C, T) → m_{10}
  273. Segment(B, A) → n_{10}
  274. Segment(A, U) → p_{10}
  275. Segment(U, B) → q_{10}
  276. Segment(C, T) → r_{10}
  277. Segment(T, D) → s_{10}
  278. Segment(D, C) → t_{10}
  279. Angle(T, D, C) → μ_2
  280. Angle(A, U, B) → ν_2
  281. Angle(B, A, U) → ξ_2
  282. Angle(T, C, D) → ο_2
  283. Segment(A, B) → a_{10}
  284. Segment(B, T) → b_{10}
  285. Segment(T, A) → c_{10}
  286. Segment(D, U) → d_{10}
  287. Segment(U, C) → e_{10}
  288. Segment(C, D) → f_{11}
  289. Angle(D, C, U) → ρ_2
  290. Angle(U, D, C) → σ_2
  291. Angle(A, T, B) → τ_2
  292. Angle(T, B, A) → υ_2
  293. Polygon(B, A, T) → t1, t_{11}, b_{11}, a_{11}
  294. Polygon(U, D, C) → t2, c_{11}, u, d_{11}
  295. InteriorAngles(t1) → ϕ_2, χ_2, ψ_2
  296. InteriorAngles(t2) → ω_2, α_3, β_3

AI Drawing Prompt Reference

Draw a quadrilateral with two diagonals intersecting at a point. Connect this intersection point to all four vertices, creating four smaller triangles. Place two small circles of equal radius at two adjacent vertices of the quadrilateral. Then, draw several segments inside the quadrilateral connecting vertices and the intersection point, and mark two angles: one at the intersection point formed by a side and a diagonal, and another at a different vertex formed by a side and a diagonal. The overall figure consists of segments, circles, and angle markers, emphasizing geometric construction relationships.
The prompt above was compiled from the original drawing commands and is for reference only.