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Angle Bisector Reflection Investigation

Angle Bisector Reflection Investigation
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2016-09-01 08:58
AngleProbability & StatisticsTransformationGeometric Construction
In collections Reflections Investigation
This example demonstrates the reflection over an angle bisector, constructing point A reflected over the bisector to explore its properties. Key math concepts include reflection, angle bisector, rotation, and special points. Construction involves commands like Polygon, Mirror, Segment, Intersect, and Angle. Suitable for high school students studying geometric transformations and probability & statistics.

GeoGebra Commands & Parameters

  1. Polygon(C, B, A) → poly1, a, c, b_1
  2. Mirror(C, f) → C'
  3. Mirror(B, f) → B'
  4. Mirror(A, f) → A'
  5. Polygon(C', B', A') → poly1', a', c', b'
  6. Segment(C, C') → CC'
  7. Segment(A, A') → AA'
  8. Segment(B, B') → BB'
  9. Intersect(CC', f) → CM
  10. Intersect(AA', f) → AM
  11. Intersect(BB', f) → BM
  12. Segment(B, BM) → MB
  13. Segment(BM, B') → MB'
  14. Segment(A, AM) → MA
  15. Segment(AM, A') → MA'
  16. Segment(C, CM) → MC
  17. Segment(CM, C') → MC'
  18. Angle(B, BM, AM) → α
  19. Angle(AM, CM, C) → β