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Pentagon Interior & Exterior Angle Sum Theorems

Pentagon Interior & Exterior Angle Sum Theorems
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2015-10-23 17:15
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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 GeoGebra applet informally illustrates to students that the sum of the measures of the interior angles of any pentagon is 540 degrees, and that the sum of the measures of the exterior angles is 360 degrees. It involves key mathematical concepts such as the interior and exterior angle sum theorems of a pentagon. Using commands like Ray, Circle, Segment, Intersect, students can dynamically explore the properties of pentagons. Suitable for middle school and above students learning geometry.

GeoGebra Commands & Parameters

  1. Ray(A, B) → a
  2. Ray(B, C) → b
  3. Ray(C, D) → c
  4. Ray(D, E) → d
  5. Ray(E, A) → e
  6. Circle(A, 1.5) → f
  7. Circle(B, 1.5) → g
  8. Circle(C, 1.5) → h
  9. Circle(D, 1.5) → k
  10. Circle(E, 1.5) → p
  11. Segment(C, A) → i
  12. Segment(C, E) → j
  13. Intersect(f, a, 1) → F
  14. Intersect(f, i, 1) → G
  15. Intersect(f, e, 1) → H
  16. Intersect(f, e, 2) → I
  17. Intersect(p, e) → J,
  18. Intersect(p, j) → K,
  19. Intersect(p, d, 1) → L
  20. Intersect(p, d, 2) → M
  21. Intersect(k, d, 1) → N
  22. Intersect(k, c, 2) → O
  23. Intersect(h, c, 1) → P
  24. Intersect(h, j, 1) → Q
  25. Intersect(h, i, 1) → R
  26. Intersect(h, b, 1) → S
  27. Intersect(g, a, 2) → T
  28. Intersect(g, b, 1) → U
  29. Intersect(g, a, 1) → V
  30. CircleSector(A, F, G) → q
  31. CircleSector(A, G, H) → r
  32. CircleSector(B, U, V) → s
  33. CircleSector(C, P, Q) → t
  34. CircleSector(C, Q, R) → c_1
  35. CircleSector(C, R, S) → d_1
  36. Intersect(k, c, 1) → W
  37. CircleSector(D, O, N) → e_1
  38. CircleSector(D, N, W) → f_1
  39. CircleSector(E, M, J) → g_1
  40. CircleSector(E, J, K) → h_1
  41. CircleSector(E, K, L) → k_1
  42. CircleSector(A, I, F) → p_1
  43. CircleSector(B, T, U) → q_1
  44. Intersect(h, b, 2) → Z
  45. CircleSector(C, Z, P) → r_1
  46. Vector(A, B) → u
  47. Vector(C, B) → v
  48. Vector(E, D) → w
  49. Vector(C, D) → u_1
  50. Vector(C, E) → v_1
  51. Vector(A, E) → w_1
  52. Translate(q, u) → q'
  53. Translate(d_1, v) → s_1
  54. Mirror(s_1, B) → t_1
  55. Dilate(A, If[0 < l ≤ 1, 1 - l, 0], B) → A'
  56. Dilate(C, If[0 < l ≤ 1, 1 - l, 0], B) → C'
  57. Dilate(A, If[1 < l ≤ 2, 2 - l, 0], E) → A'_1
  58. Dilate(C, If[1 < l ≤ 2, 2 - l, 0], E) → C'_1
  59. Dilate(C, If[2 < l ≤ 3, 3 - l, 0], D) → C'_2
  60. Dilate(E, If[2 < l ≤ 3, 3 - l, 0], D) → E'
  61. Vector(A, B) → a_1
  62. Vector(C, C') → b_1
  63. Vector(A, A'_1) → i_1
  64. Vector(E, E') → j_1
  65. Vector(C, C'_2) → l_1
  66. Vector(C, C'_1) → m_1
  67. Translate(d_1, b_1) → c_2
  68. Translate(r, i_1) → r'_1
  69. Translate(r, w_1) → r'_2
  70. Translate(k_1, w) → d_2
  71. Translate(k_1, j_1) → e_2
  72. Translate(c_1, v_1) → f_2
  73. Translate(c_1, m_1) → g_2
  74. Translate(t, u_1) → t'
  75. Translate(t, l_1) → t'_1
  76. Translate(q, a_1) → r'
  77. Translate(d_1, b_1) → h_2
  78. If(0 < l < 1, Rotate[h_2, ((l * 180))°, C']) → k_2
  79. Vector(A, A') → n_1
  80. Translate(q, n_1) → q'_1
  81. Mirror(r'_2, E) → p_2
  82. If(1 < l < 2, Rotate[r'_1, (((l - 1) * 180))°, A'_1]) → q_2
  83. Line(E, C) → a_2
  84. Mirror(t', D) → t''
  85. Line(E, D) → b_2
  86. Segment(E, C) → i_2
  87. If(2 < l < 3, Rotate[t'_1, (((l - 2) * 180))°, C'_2]) → r_2
  88. Line(E, D) → j_2
  89. Vector(D, C) → u_2
  90. Vector(E, C) → v_2
  91. Vector(A, C) → w_2
  92. Vector(B, C) → l_2
  93. Dilate(B, If[0 < o < 1, 1 - o, 0], C) → B'
  94. Dilate(A, If[1 < o < 2, 2 - o, 0], C) → A'_2
  95. Dilate(E, If[2 < o < 3, 3 - o, 0], C) → E'_1
  96. Dilate(D, If[3 < o < 4, 4 - o, 0], C) → D'
  97. Vector(B, B') → m_2
  98. Vector(A, A'_2) → n_2
  99. Vector(E, E'_1) → s_2
  100. Vector(D, D') → t_2
  101. Translate(q_1, m_2) → c_3
  102. Translate(q_1, l_2) → d_3
  103. Translate(p_1, w_2) → e_3
  104. Translate(g_1, v_2) → f_3
  105. Translate(e_1, u_2) → g_3
  106. If(1 < o < 2, Translate[p_1, n_2]) → h_3
  107. If(2 < o < 3, Translate[g_1, s_2]) → k_3
  108. If(3 < o < 4, Translate[e_1, t_2]) → p_3
  109. Point(a_2) → A_1
  110. Point(a_2) → B_1
  111. Ray(C, B_1) → a_3
  112. Ray(E, A_1) → b_3
  113. Polygon(A, B, C, D, E) → poly1, a_4, b_4, c_4, d_4, e_4
  114. Polygon(A, B, C) → poly2, c_5, a_5, b_5
  115. Polygon(A, C, E) → poly3, e_5, a_6, c_6
  116. Polygon(E, C, D) → poly4, d_5, e_6, c_7

AI Drawing Prompt Reference

Draw a pentagon ABCDE by intersecting circles centered at A, B, C, D, and E with radii of 1.5 to form the vertices. Connect these vertices to form the sides of the pentagon. Use the arc command to create the interior and exterior angles of the pentagon by connecting adjacent vertices with arcs centered at each vertex. Finally, use the vector command to draw vectors AB, BC, and ED.
The prompt above was compiled from the original drawing commands and is for reference only.