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Polygons: Sum of Exterior Angles - Quick Discovery Activity

Polygons: Sum of Exterior Angles - Quick Discovery Activity
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2017-09-19 06:52
PolygonAngleGeometric Construction
This example demonstrates the sum of exterior angles in triangles, quadrilaterals, and pentagons. Through a dynamic and modifiable figure, students can intuitively discover the pattern of the sum of exterior angles in polygons. Key mathematical concepts include polygons and angles. GeoGebra commands used include Rotate, Angle, Ray, Point, Segment, Circle, Intersect, CircleSector, Polygon, etc. Suitable for middle school and above students for geometric construction and exploration.

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