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Same Side Exterior Angles Theorem Demo

Same Side Exterior Angles Theorem Demo
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2016-09-22 02:23
AngleTransformationGeometric Construction
This example demonstrates the relationship between same side exterior angles formed by parallel lines cut by a transversal; core math concepts include properties of parallel lines, same side exterior angle theorem, and angle measurement; construction highlights the use of GeoGebra commands/objects like Point, Rotate, Angle, Line, Circle, Intersect, CircleSector, Dilate, Vector, Translate, CircleArc; suitable for high school geometry education to visually understand the theorem and its applications.

GeoGebra Commands & Parameters

  1. Point(a) → B
  2. Rotate(B, α, A) → B'
  3. Angle(B, A, B') → β
  4. Line(A, B') → b
  5. Circle(A, 1) → e
  6. Intersect(b, d) → C
  7. Circle(C, 1) → f
  8. Intersect(e, a) → D, E
  9. Intersect(e, b) → F, G
  10. Intersect(f, b) → H, I
  11. Intersect(f, d) → J, K
  12. CircleSector(C, K, I) → g
  13. CircleSector(C, I, J) → h
  14. CircleSector(C, J, H) → k
  15. CircleSector(C, H, K) → p
  16. CircleSector(A, D, F) → s
  17. CircleSector(A, F, E) → t
  18. Dilate(A, If[0 < i < 1, 1 - i], C) → A'
  19. Vector(A, A') → u
  20. Translate(s, u) → s'
  21. Translate(t, u) → t'
  22. CircleArc(C, K, I) → d_1
  23. CircleArc(C, I, J) → e_1
  24. CircleArc(A, D, F) → g_1
  25. CircleArc(A, F, E) → k_1