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Geometric Rotation Transformation: Polygon Rotation Demo

Geometric Rotation Transformation: Polygon Rotation Demo
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2015-09-21 21:58
PolygonAngleTransformationGeometric ConstructionSlider Animation
This example demonstrates the dynamic geometric construction of rotating a polygon around a specified center point O. The core mathematical concept is rotation transformation—rotation preserves the shape and size of a figure while only changing its position and direction, involving elements such as rotation angle, center of rotation, and corresponding points before and after rotation. Construction key points: Use GeoGebra's Rotate command to rotate polygon poly1 around center point O by angle α to obtain poly1', simultaneously showing the transformation relationships of corresponding points A→A', B→B', C→C', with adjustable rotation angle via sliders. Suitable for middle school geometry teaching, rotation concept explanation, and geometric construction training.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a_1, b_1
  2. Rotate(A, α, O) → A'
  3. Rotate(B, α, O) → B'
  4. Rotate(C, α, O) → C'
  5. Polygon(A', B', C') → poly1', c', a', b'
  6. Segment(A, O) → f
  7. Segment(O, A') → g
  8. Angle(A, O, A') → β
  9. AngularBisector(f, g) → h, i
  10. Point(i) → D
  11. Angle(A', O, A) → γ
  12. Point(i) → E
  13. Segment(O, C) → j