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Exterior Angles Investigation by Tim Brzezinski

Exterior Angles Investigation by Tim Brzezinski
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2018-03-20 09:50
PolygonAngleInequalityGeometric Construction
In collections Polygons & Angles
This example demonstrates the properties and sum of exterior angles in polygons. It covers core concepts like the exterior angle theorem, relationships between interior and exterior angles, and inequalities. Construction involves commands such as Ray, Polygon, Circle, Intersect, CircleSector, Dilate, Vector, Translate, and Angle to dynamically create and modify polygons and their exterior angles. Suitable for high school mathematics education, fostering exploratory learning and concept comprehension.

GeoGebra Commands & Parameters

  1. Ray(A, B) → f
  2. Ray(B, C) → g
  3. Ray(C, A) → h
  4. Polygon(A, B, C) → t1, c, a, b
  5. Min({a, b, c}) → d
  6. Circle(C, (0.25 * d)) → e
  7. Circle(A, (0.25 * d)) → k
  8. Circle(B, (0.25 * d)) → p
  9. Intersect(e, g, 2) → E
  10. Intersect(e, h, 1) → F
  11. Intersect(k, h, 2) → G
  12. Intersect(k, f, 1) → H
  13. Intersect(p, f, 2) → I
  14. Intersect(p, g, 1) → J
  15. CircleSector(C, E, F) → q
  16. CircleSector(A, G, H) → r
  17. CircleSector(B, I, J) → s
  18. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], D) → A'
  19. Dilate(B, If[0 < u ≤ 1, 1 - u, 0], D) → B'
  20. Dilate(C, If[0 < u ≤ 1, 1 - u, 0], D) → C'
  21. Vector(C, C') → v
  22. Vector(A, A') → w
  23. Vector(B, B') → i
  24. Translate(q, v) → q'
  25. Translate(r, w) → r'
  26. Translate(s, i) → s'
  27. CircleSector(C, F, E) → t
  28. CircleSector(A, H, G) → c_1
  29. CircleSector(B, J, I) → d_1
  30. Angle(A, C, B) → α
  31. Translate(c_1, w) → e_1
  32. Translate(t, v) → t'
  33. Translate(d_1, i) → f_1
  34. Translate(B, i) → B'_1
  35. Translate(C, i) → C'_1
  36. Ray(B'_1, C'_1) → g'
  37. Translate(C, v) → C'_2
  38. Translate(A, v) → A'_1
  39. Ray(C'_2, A'_1) → h'
  40. Translate(A, w) → A'_2
  41. Translate(B, w) → B'_2
  42. Ray(A'_2, B'_2) → f'
  43. Polygon(A'_2, B'_1, C'_2) → t2, c'_2, a'_2, b'_1