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Similar Triangles and Dilation

Similar Triangles and Dilation
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2015-12-18 05:07
TriangleTransformationGeometric Construction
This example demonstrates the properties and graphical changes of similar triangles under dilation transformations. Key math concepts include similarity criteria, dilation transformations, angle and side length ratios. Construction highlights from the summary involve GeoGebra commands like Intersect, Circle, Point, Segment, Dilate, Rotate, Angle, Line, Polygon, Vector, and Translate. Suitable for high school mathematics instruction on geometric transformations and similarity.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, d_1) → c
  3. Point(c) → B
  4. Segment(A, B) → a_2
  5. Circle(B, e) → f
  6. Dilate(A, d, A) → A'_1
  7. Dilate(B, d, A) → B'
  8. Rotate(A, angleB, B) → A'_2
  9. Angle(A, B, A'_2) → β
  10. Line(B, A'_2) → b
  11. Intersect(f, b, 2) → C
  12. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  13. Dilate(A, d, A) → A'
  14. Dilate(B, d, A) → B'_1
  15. Dilate(C, d, A) → C'
  16. Polygon(A', B'_1, C') → poly1', c', a', b'_1
  17. Vector(F, G) → v
  18. Translate(A', v) → K
  19. Translate(B'_1, v) → H
  20. Translate(C', v) → J
  21. Polygon(K, H, J) → poly1'', c'', a'', h
  22. Angle(B, C, A) → α
  23. Angle(K, H, J) → γ
  24. Angle(H, J, K) → δ