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Exterior Angle Sum of Triangles and Polygons

Exterior Angle Sum of Triangles and Polygons
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2020-03-22 18:37
TrianglePolygonAngleSlider Animation
This example demonstrates the exterior angle sum of triangles, quadrilaterals, and pentagons. Through a dynamically modifiable figure, it quickly reveals the pattern of exterior angle sums. Key mathematical concepts include angles, polygons, and triangles. GeoGebra commands used include Rotate, Angle, Ray, Point, Segment, and others. Suitable for middle school and above students to learn geometric construction and the properties of exterior angle sums.

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[0 < a ≤ 1, 1 - a, 0], B) → A'_1
  28. Vector(A, A'_1) → u
  29. Dilate(B, If[1 < a ≤ 2, 2 - 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