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Exterior Angles of a Triangle Activity

Exterior Angles of a Triangle Activity
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2017-06-12 08:21
TriangleAngleTrigonometryGeometric ConstructionSlider Animation
In collections Congruence (CO) Cluster Polygons & Angles Polygons & Angles ( s n attar) Polygons & Angles
This example demonstrates the properties and sum relationships of exterior angles in a triangle. Core math concepts include the exterior angle theorem and the triangle angle sum theorem. Construction highlights the use of GeoGebra commands like Rotate, Angle, Ray, Point, Segment, Circle, Intersect, CircleSector, Polygon, Dilate, Vector, and Translate. Suitable for middle school and above mathematics education, ideal for dynamic exploration of geometric properties.

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