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Triangle Interior & Exterior Angle Sum Theorems (II)

Triangle Interior & Exterior Angle Sum Theorems (II)
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2015-11-20 03:16
TriangleAngleTransformationGeometric Construction
In collections Polygons & Angles Polygons & Angles Polygons & Angles Geometry: Polygons & Angles Geometry: Polygons & Angles
This GeoGebra applet demonstrates the Triangle Interior Angle Sum Theorem and Exterior Angle Theorem. It visualizes how the sum of interior angles equals 180 degrees and how an exterior angle relates to remote interior angles. Construction utilizes commands like Ray, Point, Angle, Polygon, Rotate, and Translate to create interactive geometric figures. Ideal for middle school geometry students and educators to explore angle properties dynamically.

GeoGebra Commands & Parameters

  1. Ray(A, B) → a
  2. Ray(B, C) → b
  3. Ray(C, A) → c
  4. Point(a) → D_1
  5. Point(b) → E_1
  6. Point(c) → F_1
  7. Ray(A, F_1) → d
  8. Ray(B, D_1) → e
  9. Ray(C, E_1) → f
  10. Point(e) → D
  11. Point(f) → E
  12. Point(d) → F
  13. Angle(B, A, C) → α
  14. Angle(C, B, A) → β
  15. Angle(A, C, B) → γ
  16. Angle(F, A, B) → δ
  17. Angle(D, B, C) → ε
  18. Angle(E, C, A) → ζ
  19. Circle(A, 1.5) → g
  20. Circle(B, 1.5) → h
  21. Circle(C, 1.5) → k
  22. Intersect(g, c, 1) → G
  23. Intersect(g, a, 1) → H
  24. Intersect(g, c, 2) → I
  25. Intersect(h, b, 1) → J
  26. Intersect(h, a, 1) → K
  27. Intersect(h, a, 2) → L
  28. Intersect(k, b) → M, N
  29. Intersect(k, c) → O,
  30. CircleSector(A, H, G) → p
  31. CircleSector(B, J, K) → q
  32. CircleSector(C, O, M) → r
  33. CircleSector(C, N, O) → s
  34. CircleSector(B, L, J) → t
  35. CircleSector(A, I, H) → c_1
  36. Line(C, a) → i
  37. Vector(B, C) → u
  38. Vector(A, C) → v
  39. Translate(q, u) → q'
  40. Segment(B, C) → l
  41. Dilate(C, If[0 < j ≤ 1, j, 0], B) → C'
  42. Vector(B, C') → w
  43. Translate(q, w) → q'_1
  44. Rotate(q'_1, If[0 < j, (((-j) * 180))°, 180*°], C') → d_1
  45. Mirror(q', C) → q''
  46. Dilate(A, If[1 < j ≤ 2, 2 - j, 0], C) → C'_1
  47. Vector(A, C'_1) → m
  48. Translate(p, m) → p'
  49. Dilate(C, If[0 < n ≤ 1, n, 0], B) → C'_2
  50. Dilate(A, If[1 < n ≤ 2, 2 - n, 0], C) → A'
  51. Vector(B, C'_2) → u_1
  52. Vector(A, A') → v_1
  53. If(0 < n ≤ 1, Translate[t, u_1], Translate[t, u]) → e_1
  54. If(1 < n ≤ 2, Translate[c_1, v_1], Translate[c_1, v]) → f_1
  55. Polygon(A, B, C) → poly1, c_2, a_2, b_1
  56. Line(A, B) → g_1
  57. Segment(C, B) → j_1
  58. Ray(B, C) → k_1
  59. Midpoint(B, C) → P
  60. Segment(C, P) → l_1
  61. Segment(P, B) → m_1
  62. If(0 < j < 1, Rotate[B, ((j * 180))°, P]) → Q
  63. If(0 < j < 1, Rotate[q, ((j * 180))°, P]) → p_1
  64. If(0 < j < 1, Segment[Rotate[A, ((j * 180))°, P], Rotate[B, ((j * 180))°, P]]) → r_1
  65. Rotate(A, 180*°, P) → A'_1
  66. Rotate(B, 180*°, P) → B'
  67. Segment(A'_1, B') → s_1
  68. Segment(C, B) → t_1
  69. Segment(B, A) → q_1
  70. Segment(B, A) → b_2
  71. Midpoint(A, C) → R
  72. Segment(A, R) → d_2
  73. Segment(R, C) → e_2
  74. Segment(A, C) → h_2
  75. If(1 < j ≤ 2, Rotate[p, (((-(j - 1)) * 180))°, R]) → f_2
  76. Segment(A, C) → i_2
  77. If(1 < j ≤ 2, Segment[Rotate[A, (((-(j - 1)) * 180))°, R], Rotate[C, (((-(j - 1)) * 180))°, R]]) → j_2
  78. If(0 < j ≤ 1, Segment[Rotate[C, ((j * 180))°, P], Rotate[B, ((j * 180))°, P]]) → k_2
  79. If(1 < j ≤ 2, Segment[Rotate[B, (((-(j - 1)) * 180))°, R], Rotate[A, (((-(j - 1)) * 180))°, R]]) → i_1
  80. Ray(B, C) → n_1
  81. Ray(A, B) → g_2
  82. Ray(C, A) → l_2

AI Drawing Prompt Reference

Draw a triangle ABC with rays a, b, and c through points A, B, and C. Construct angles α, β, γ, δ, ε, and ζ using points A, B, C, and D, E, F. Draw circles centered at A, B, and C, and find intersection points G, H, I, J, K, L, M, N, and O. Use these points to construct sectors p, q, r, s, t, and c_1. Draw a line i through point C and use vectors u and v to construct new rays and sectors. Finally, use rotation, mirroring, and scaling to construct new sectors d_1 and q'', as well as new point C'_1 and sector p'.
The prompt above was compiled from the original drawing commands and is for reference only.