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Rotation with Variable Angle

Rotation with Variable Angle
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2015-02-21 06:57
AngleTransformationGeometric Construction
This example demonstrates the phenomenon of rotating shapes with varying angles. Key mathematical concepts include rotation, angle, and geometric transformations. Using GeoGebra commands such as Point, Polygon, Segment, Rotate, and Angle, dynamic rotating shapes can be constructed. Suitable for middle school and above students to learn about geometric transformations and dynamic geometry.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 3.1622776601683795]) → B
  2. Polygon(A, B, C, D, E) → poly1, a, b, c, d, e
  3. Segment(F, A) → f
  4. Rotate(A, β, F) → A'
  5. Rotate(B, β, F) → B'
  6. Rotate(C, β, F) → C'
  7. Rotate(D, β, F) → D'
  8. Rotate(E, β, F) → E'
  9. Polygon(A', B', C', D', E') → poly1', a', b', c', d', e'
  10. Segment(F, A') → g
  11. Angle(A, F, A') → β_1

AI Drawing Prompt Reference

Draw a pentagon with a line segment from one of its vertices as the axis of rotation, then rotate the pentagon by a variable angle to show the comparison between the original and rotated shapes, including the angle and axis segment.
The prompt above was compiled from the original drawing commands and is for reference only.