Intersecting Reflections II

Intersecting Reflections II
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2017-07-12 17:27
This example demonstrates the process of constructing complex geometric shapes through reflections and rotations. It involves core mathematical concepts such as reflection transformations, linear functions, power functions, and parabolas in solid geometry. The construction utilizes GeoGebra commands like Line, Rotate, Mirror, Segment, and Angle, along with objects O, P, line_1, α, P', line_2, A, A', A'', f, g, h, β, a_1, and text1. It is suitable for high school and above students exploring the interaction between spatial geometry and function graphs.

GeoGebra Commands & Parameters

  1. Line(O, P) → line_1
  2. Rotate(P, α, O) → P'
  3. Line(P', O) → line_2
  4. Mirror(A, line_1) → A'
  5. Mirror(A', line_2) → A''
  6. Segment(A, O) → f
  7. Segment(O, A'') → g
  8. Segment(O, A') → h
  9. Angle(A, O, A'') → β
  10. Angle(P, O, P') → a_1