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Exterior Angles of Polygons by Tim Brzezinski

Exterior Angles of Polygons by Tim Brzezinski
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2017-07-16 21:23
PolygonAngleGeometric ConstructionSlider Animation
In collections Congruence (CO) Cluster Polygons & Angles Polygons & Angles ( s n attar) Polygons & Angles Year 9 Mathematics
This example demonstrates the exterior angles of triangles, quadrilaterals, and pentagons, allowing quick discovery through dynamic and modifiable activities. It covers core concepts like the sum of exterior angles and the relationship between interior and exterior angles. Constructed using commands such as Rotate, Angle, Ray, Point, Segment, Min, Circle, Intersect, CircleSector, Polygon, Dilate, Vector, and Translate, it is suitable for middle school and higher education to explore polygon properties interactively.

GeoGebra Commands & Parameters

  1. Rotate(A, (b * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Ray(B, A) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Segment(C, A) → h
  7. Segment(B, C) → i
  8. Segment(B, A) → j
  9. Min({j, i, h}) → c
  10. Ray(C, A) → k
  11. Ray(A, B) → l
  12. Circle(B, (0.2 * c)) → d
  13. Circle(A, (0.2 * c)) → e
  14. Circle(C, (0.2 * c)) → p
  15. Intersect(e, l, 1) → D
  16. Intersect(e, k, 2) → E
  17. Intersect(d, l, 2) → F
  18. Intersect(g, i) → G
  19. Intersect(g, i) → H
  20. Intersect(d, g, 1) → I
  21. Intersect(p, k) → J,
  22. Intersect(p, g) → K, L
  23. CircleSector(B, I, F) → q
  24. CircleSector(C, J, L) → r
  25. CircleSector(A, D, E) → s
  26. Polygon(B, A, C) → poly1, c_1, b_1, a_1
  27. Dilate(A, If[1 < a ≤ 2, 2 - a, 0], B) → A'_1
  28. Vector(A, A'_1) → u
  29. Dilate(B, If[3 < a ≤ 4, 4 - a, 0], C) → B'
  30. Vector(B, B') → v
  31. Translate(q, v) → q'
  32. Translate(s, u) → s'
  33. Translate(s', v) → s''
  34. Translate(q, v) → q'_1
  35. CircleArc(A, D, E) → t
  36. CircleArc(B, I, F) → d_1
  37. Angle(B, A, E) → β
  38. Angle(C, B, F) → γ
  39. Angle(A, C, L) → δ
  40. Rotate(E, If[0 < a ≤ 1, (-((a * β))), (-β)], A) → E'
  41. CircleSector(A, E', E) → e_1
  42. Translate(e_1, u) → f_1
  43. Rotate(F, If[2 < a ≤ 3, ((-(a - 2)) * γ), (-γ)], B) → F'
  44. CircleSector(B, F', F) → g_1
  45. Translate(g_1, v) → h_1
  46. Translate(f_1, v) → k_1
  47. Rotate(L, If[4 < a ≤ 5, ((-(a - 4)) * δ), (-δ)], C) → L'
  48. CircleSector(C, L', L) → p_1

AI Drawing Prompt Reference

Create an interactive diagram showing exterior angles of polygons. Start with a triangle where one vertex can slide along a ray to change its shape. At each vertex, draw an arc representing the exterior angle and fill it with a colored sector. Show translation arrows from vertices to illustrate how exterior angles can be rearranged. Use a slider to switch between triangle, quadrilateral, and pentagon, dynamically demonstrating that the sum of exterior angles is always 360 degrees. Include clear vertex labels, angle arcs, and auxiliary rays for educational clarity.
The prompt above was compiled from the original drawing commands and is for reference only.