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Rectangle - Point Symmetry

Rectangle - Point Symmetry
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2018-08-23 12:08
Coordinate GeometryTransformationGeometric Construction
This example demonstrates point symmetry in a rectangle, illustrating the positional relationship between symmetric points through rotation and construction. Core mathematical concepts include symmetry, rotation, geometric construction, and coordinate geometry. The construction uses GeoGebra commands like Segment and Rotate, involving objects such as A, B, C, D, E, α, C', D', i, D'_1, etc. Suitable for high school mathematics teaching to understand geometric transformations and symmetry.

GeoGebra Commands & Parameters

  1. Segment(D, A) → f
  2. Segment(A, B) → g
  3. Segment(B, C) → h
  4. Segment(C, D) → i
  5. Rotate(C, α, E) → C'
  6. Rotate(D, α, E) → D'
  7. Segment(C', D') → i'
  8. Rotate(D, α, E) → D'_1
  9. Rotate(A, α, E) → A'
  10. Segment(D'_1, A') → f'
  11. Rotate(A, α, E) → A'_1
  12. Rotate(B, α, E) → B'
  13. Segment(A'_1, B') → g'
  14. Rotate(B, α, E) → B'_1
  15. Rotate(C, α, E) → C'_1
  16. Segment(B'_1, C'_1) → h'

AI Drawing Prompt Reference

Draw a rectangle ABCD, then rotate it 180 degrees around point E to generate the symmetric rectangle A'B'C'D'. First, draw the four sides of the rectangle, then rotate points C and D to generate C' and D', connect C' and D', rotate points A and B to generate A' and B', and finally connect A' and B'.
The prompt above was compiled from the original drawing commands and is for reference only.