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Exploring Similar Polygons Under Dilation

Exploring Similar Polygons Under Dilation
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2018-11-21 06:39
PolygonAngleTransformationGeometric Construction
This example demonstrates how the properties of polygons change under similarity transformations (dilations), focusing on vertex coordinates, side lengths, and angle measures. Key math concepts include similarity transformation, dilation center, scale factor, and corresponding side-angle relationships. The construction uses commands like Line, OrthogonalLine, Point, Polygon, Angle, Segment, and Dilate, with a slider k to adjust the scale factor dynamically. Suitable for high school geometry instruction to understand the properties and characteristics of similar figures and transformations.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → C
  4. Line(C, a) → c
  5. Point(c) → D
  6. Polygon(A, B, C, D) → poly1, a_1, b_1, c_1, d
  7. Point(b) → O
  8. Angle(C, B, A) → α
  9. Segment(A, B) → e
  10. Segment(D, C) → f
  11. Dilate(A, k, O) → A'
  12. Dilate(B, k, O) → B'
  13. Dilate(C, k, O) → C'
  14. Dilate(D, k, O) → D'
  15. Polygon(A', B', C', D') → poly1', a', b', c', d'
  16. Dilate(A, k, O) → A'_1
  17. Dilate(B, k, O) → B'_1
  18. Segment(A'_1, B'_1) → e'
  19. Dilate(D, k, O) → D'_1
  20. Dilate(C, k, O) → C'_1
  21. Segment(D'_1, C'_1) → f'
  22. Angle(C', B', A') → β