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Heptagon Angle Sum Theorems Demo

Heptagon Angle Sum Theorems Demo
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2015-10-29 01:00
PolygonAngleGeometric ConstructionSlider Animation
In collections Polygons & Angles Polygons & Angles Polygons & Angles ( s n attar) Polygons & Angles Polygons & Angles Polygons & Angles Polygons & Angles Geometry: Polygons & Angles Geometry: Polygons & Angles
This applet informally illustrates to students that the sum of the measures of the interior angles of any heptagon is 180*5=900 degrees, and that the sum of the exterior angles is always 360 degrees. It covers core math concepts like polygon angle sum theorems, exterior angle properties, and angle calculations. The construction uses GeoGebra commands such as Ray, Circle, Intersect, Segment, CircleSector, Vector, Translate, Mirror, Dilate, If, Rotate, Polygon, and Point. Suitable for high school students learning polygon geometry and for classroom demonstrations.

GeoGebra Commands & Parameters

  1. Ray(N_1, D) → l_4
  2. Circle(D, 1.5) → k
  3. Intersect(k, l_4) → W_1, Z_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. Ray(C, E) → 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, H_2
  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, Z_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. Circle(N_1, 1.5) → d_5
  160. Intersect(d_5, i_4, 2) → K_1
  161. Intersect(d_5, l_4, 1) → O_1
  162. Intersect(d_5, i_4, 1) → P_1
  163. Intersect(h, i_4, 1) → Q_1
  164. CircleSector(C, Q_1, P) → f_5
  165. CircleSector(N_1, O_1, P_1) → g_5
  166. Intersect(k, l_4, 1) → R_1
  167. CircleSector(D, E_1, R_1) → h_5
  168. Dilate(D, If[4 < l < 5, 5 - l, 0], N_1) → D'_2
  169. Dilate(C, If[4 < l < 5, 5 - l, 0], N_1) → C'_5
  170. Vector(C, N_1) → w_4
  171. Vector(D, N_1) → j_4
  172. Translate(f_5, w_4) → k_5
  173. Translate(h_5, j_4) → p_5
  174. Mirror(p_5, N_1) → q_5
  175. Vector(D, D'_2) → m_4
  176. Vector(C, C'_5) → n_4
  177. Translate(h_5, m_4) → r_5
  178. Translate(f_5, n_4) → s_5
  179. Rotate(r_5, If[4 < l < 5, (((l - 4) * 180))°, 0], D'_2) → t_5
  180. Polygon(D, C, N_1) → poly5, n_5, d_6, c_8
  181. Segment(D, C) → b_5
  182. Ray(C, E) → i_5
  183. Ray(C, A_1) → j_5
  184. Ray(C, D) → l_5
  185. Point(j_5) → T_1
  186. Point(l_5) → U_1
  187. Ray(A_1, T_1) → m_5
  188. Ray(D, U_1) → b_6
  189. Polygon(A_1, E, A, B, C, N_1, D) → poly6, a_8, e_6, a_9, b_7, c_9, n_6, d_7
  190. Intersect(d_5, l_4, 1) → S_1
  191. Intersect(d_5, i_4, 2) → V_1
  192. CircleSector(N_1, V_1, S_1) → f_6
  193. CircleSector(C, Z, Q_1) → r_1
  194. Vector(N_1, C) → u_5
  195. Translate(f_6, u_5) → g_6
  196. Dilate(N_1, If[5 < o < 6, 6 - o, 0], C) → A_2
  197. Vector(N_1, A_2) → v_5
  198. Translate(f_6, v_5) → h_6
  199. Vector(D, C) → w_5
  200. Translate(h_4, w_5) → k_6