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Invariance of Angles under Dilation Transformation

Invariance of Angles under Dilation Transformation
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2017-01-31 19:39
PolygonAngleTransformationGeometric Construction
This example demonstrates the invariance of angles under dilation transformations. Core concepts include similarity, geometric transformations, and angle preservation. Construction involves creating a polygon for the original triangle, using the Dilate command with a scale factor and center to generate the image triangle, and measuring angles with Segment and Angle tools. Suitable for high school geometry students to visualize properties of similar figures.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → Original, c, a_1, b
  2. Dilate(A, ScaleFactor, Center) → A'
  3. Dilate(B, ScaleFactor, Center) → B'
  4. Dilate(C, ScaleFactor, Center) → C'
  5. Polygon(A', B', C') → Image, c', a', b'
  6. Segment(Center, A') → f
  7. Segment(Center, B') → g
  8. Segment(Center, C') → h
  9. Angle(C, B, A) → α
  10. Angle(B, A, C) → β
  11. Angle(B', A', C') → γ
  12. Angle(C', B', A') → δ
  13. Angle(A', C', B') → ε
  14. Angle(A, C, B) → ζ