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Alternate Exterior Angles Theorem Demo by Jerry Gallaher

Alternate Exterior Angles Theorem Demo by Jerry Gallaher
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2016-09-22 02:20
AngleTransformationGeometric Construction
This example demonstrates the relationship between alternate exterior angles formed when parallel lines are cut by a transversal. It involves core math concepts like parallel line properties, corresponding angles, alternate interior angles, and the theorem itself. Construction uses commands/objects such as Point, Rotate, Angle, Line, Circle, Intersect, CircleSector, Dilate, Vector, Translate, CircleArc. Suitable for middle school and above students to understand and verify geometric theorems.

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. Vector(A, C) → v
  25. Translate(s, v) → s'_1
  26. Rotate(s'_1, (((i - 1) * 180))°, C) → k
  27. Translate(t, v) → t'_1
  28. Rotate(t'_1, (((-(i - 1)) * 180))°, C) → p