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Alternate Exterior Angles Theorem

Alternate Exterior Angles Theorem
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2016-02-05 11:17
AngleTransformationGeometric Construction
In collections Parallel Lines & Related Angles Parallel Lines & Related Angles Geometry: Parallel Lines & Related Angles Angle Congruence Intros
This example illustrates the Alternate Exterior Angles Theorem, which states that when two parallel lines are cut by a transversal, the alternate exterior angles are equal. Key mathematical concepts include parallel lines and alternate exterior angles. The construction uses GeoGebra commands such as Point, Rotate, Angle, etc. Suitable for middle school and above students learning geometry.

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(A, D, F) → s
  15. CircleSector(A, F, E) → t
  16. Dilate(A, If[0 < i < 1, 1 - i], C) → A'
  17. Vector(A, A') → u
  18. Translate(s, u) → s'
  19. Translate(t, u) → t'
  20. CircleArc(C, K, I) → d_1
  21. CircleArc(C, I, J) → e_1
  22. CircleArc(A, D, F) → g_1
  23. CircleArc(A, F, E) → k_1
  24. Rotate(s', ((i * 180))°, A') → s''
  25. Rotate(t', ((i * 180))°, A') → t''