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Obvious Corollary: Dynamic Illustration of Triangle Exterior Angle Theorem

Obvious Corollary: Dynamic Illustration of Triangle Exterior Angle Theorem
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2016-11-13 03:42
TriangleAngleTransformationGeometric ConstructionSlider Animation
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Triangle Theorems Unit 7: Polygons and Quadrilaterals
This GeoGebra example dynamically illustrates an obvious corollary to the Triangle-Angle-Sum Theorem: the measure of an exterior angle of a triangle equals the sum of the measures of the two non-adjacent interior angles. The interactive construction allows learners to drag points and observe how angle relationships remain invariant. Core mathematical concepts include triangle angle sum, exterior angle theorem, angle measurement, and rotation. The construction uses GeoGebra commands such as Ray, Point, Rotate, Segment, Angle, Polygon, Circle, Intersect, Dilate, Min, CircleSector, Vector, Translate, Line, and CircleArc to build multiple triangles, auxiliary circles, angle markers, and dynamic points. Suitable for middle school or high school geometry classes, this resource is ideal for classroom demonstration or self-paced exploration, reinforcing the connection between the triangle angle sum and its corollaries.

GeoGebra Commands & Parameters

  1. Ray(E, L) → l
  2. Point(l) → M
  3. Rotate(M, α, E) → M'
  4. Ray(E, M') → m
  5. Point(y = 0) → A
  6. Segment(A, C) → j
  7. Rotate(C, α, A) → C'
  8. Ray(A, C') → g
  9. Point(g) → D
  10. Segment(A, D) → i
  11. Segment(D, C) → h
  12. Ray(A, C) → f
  13. Angle(C, A, C') → β
  14. Polygon(A, C, D) → poly1, d, a, c
  15. Angle(M, E, M') → γ
  16. Circle(E, i) → e
  17. Circle(E, j) → k
  18. Intersect(k, l, 1) → F
  19. Intersect(e, m, 1) → G
  20. Circle(G, 1) → p
  21. Circle(F, 1) → q
  22. Circle(G, h) → r
  23. Intersect(r, l) → H, U
  24. Dilate(G, b, E) → G'
  25. Dilate(H, b, E) → H'
  26. Segment(G', H') → n
  27. Polygon(E, H', G') → poly2, g', e_1, h'
  28. Angle(poly2) → δ, ε, ζ
  29. Angle(poly1) → η, θ, ι
  30. Segment(E, H') → s
  31. Segment(E, G') → t
  32. Min({j, i, h}) → o
  33. Circle(A, (0.2 * o)) → c_1
  34. Circle(D, (0.2 * o)) → d_1
  35. Circle(C, (0.2 * o)) → f_1
  36. Intersect(c_1, j, 1) → I
  37. Intersect(c_1, i, 1) → J
  38. Intersect(d_1, i, 1) → K
  39. Intersect(d_1, h, 1) → N
  40. Intersect(f_1, h, 1) → O
  41. Intersect(j, xAxis) → P
  42. Intersect(f_1, j, 1) → Q
  43. CircleSector(A, I, J) → g_1
  44. CircleSector(D, K, N) → h_1
  45. CircleSector(C, O, Q) → k_1
  46. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], E) → A'
  47. Vector(A, A') → v
  48. Translate(g_1, v) → p_1
  49. Line(A, t) → i_1
  50. Point(i_1) → R
  51. Angle(D, A, R) → κ
  52. Rotate(p_1, If[1 < u ≤ 2, ((u - 1) * κ), κ], E) → q_1
  53. Dilate(D, If[2 < u ≤ 3, 3 - u, 0], G') → D'
  54. Vector(D, D') → w
  55. Translate(h_1, w) → r_1
  56. Line(D, n) → j_1
  57. Point(j_1) → S
  58. Angle(N, D, S) → λ
  59. Rotate(r_1, If[3 < u ≤ 4, ((u - 3) * λ), λ], G') → s_1
  60. Dilate(C, If[6 < u ≤ 7, 7 - u, 0], H') → C'_1
  61. Vector(C, C'_1) → u_1
  62. Translate(k_1, u_1) → t_1
  63. Line(C, s) → l_1
  64. Point(l_1) → T
  65. Angle(A, C, T) → μ
  66. Rotate(t_1, If[7 < u ≤ 8, ((u - 7) * μ), μ], H') → c_2
  67. CircleArc(A, I, J) → d_2
  68. CircleArc(D, K, N) → e_2
  69. CircleArc(C, O, Q) → f_2

AI Drawing Prompt Reference

Draw a triangle with draggable vertices to dynamically show that an exterior angle equals the sum of the two opposite interior angles. Mark the exterior and interior angles with sectors and angle indicators. Include auxiliary lines, circles, and points to illustrate the relationship. Use a slider to control rotation and dynamic points for key positions. The final image should clearly demonstrate the theorem, suitable for geometry class demonstration.
The prompt above was compiled from the original drawing commands and is for reference only.