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Perpendicular Reflections Investigation

Perpendicular Reflections Investigation
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2016-09-01 09:15
VectorTransformationGeometric Construction
In collections Reflections Investigation
This example demonstrates the geometric phenomenon of constructing perpendicular lines through reflections. It involves core math concepts like reflection, vectors, subtraction, and geometric transformations. The construction utilizes commands/objects such as Polygon, Mirror, Segment, Intersect, Angle, and Point as outlined in the summary. Suitable for high school students and teachers learning about geometric transformations and vectors.

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
  20. Angle(A, AM, CM) → γ
  21. Point(f) → D
  22. Angle(D, BM, B) → δ