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Polygons: Exterior Angles - Triangle, Quadrilateral, Pentagon Discovery

Polygons: Exterior Angles - Triangle, Quadrilateral, Pentagon Discovery
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2018-04-18 01:39
TrianglePolygonAngleTransformationGeometric Construction
This GeoGebra applet demonstrates the exterior angles of triangles, quadrilaterals, and pentagons. It covers core math concepts like polygon exterior angle sum theorem, plane geometry, and angle measurement. Construction utilizes commands such as Rotate, Angle, Ray, Polygon, Vector, and Intersect to create a dynamic, modifiable model. Ideal for middle school geometry students or teachers for interactive classroom demonstrations to visualize why the sum of exterior angles is always 360 degrees.

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