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Similarity by Side Ratios

Similarity by Side Ratios
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2014-12-04 06:22
TriangleTransformationGeometric ConstructionSlider Animation
① This example dynamically demonstrates the side-ratio criterion for triangle similarity: when the three corresponding side lengths are proportional, the two triangles are similar. ② Core mathematical concepts include the SSS similarity theorem, ratios, corresponding sides, similarity ratio, and dilation (homothety) transformations. ③ Construction details: GeoGebra commands such as Textfield (for user input of side ratios), Point, Circle, Intersect, Line, Polygon, and Distance are used to build two triangles; the Dilation tool or similar transformation generates corresponding points A', B', C', and the dynamic updates show the similarity relationship as ratios change. ④ Suitable for middle school geometry lessons or high school review, this interactive tool helps students explore and verify the side-ratio condition for similarity, making abstract concepts tangible.

GeoGebra Commands & Parameters

  1. Textfield(S_1) → inputBox1
  2. Textfield(S_2) → inputBox2
  3. Textfield(S_3) → inputBox3
  4. Point(Circle[A, S_1]) → B
  5. Circle(A, S_2) → e
  6. Circle(B, S_3) → g
  7. Intersect(e, g, 1) → C
  8. Point(Circle[A', k * S_1]) → B'
  9. Circle(A', k * S_2) → c
  10. Circle(B', k * S_3) → d
  11. Intersect(c, d, 1) → C'
  12. Textfield(k) → inputBox4
  13. Line(A, B) → r
  14. Circle(A, k * S_1) → s
  15. Intersect(s, r, 2) → B''
  16. Circle(A, k * S_2) → d_1
  17. Circle(B'', k * S_3) → t
  18. Intersect(d_1, t, 1) → C''
  19. Polygon(A, B, C) → poly1, c_2, a_2, b_2
  20. Polygon(A, B'', C'') → poly2, c'', a_3, b''
  21. Polygon(A', B', C') → poly3, c', a', b'
  22. Distance(a_2, c_2) → a
  23. Distance(c', b_2) → b
  24. Distance(b', a') → h
  25. Distance(c'', b'') → j

AI Drawing Prompt Reference

Draw two similar triangles. The first triangle is formed by points A, B, and C. The second triangle is formed by points A, B'', and C''. The triangles should be related by a scaling transformation, with the scaling ratio determined by user-input side ratios. The drawing should show the proportional relationship between the sides of the two triangles and label the scaling ratio.
The prompt above was compiled from the original drawing commands and is for reference only.