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Making Similar Triangles 3: Dynamic Construction and Parametric Exploration

Making Similar Triangles 3: Dynamic Construction and Parametric Exploration
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2019-04-07 22:18
TriangleTransformationParametric EquationGeometric ConstructionSlider Animation
In collections Making Similar Triangles
This GeoGebra example demonstrates how to dynamically construct a series of similar triangles using parametric controls and similarity transformations. The core mathematical concepts include similar triangles, similarity transformations (rotation, scaling, and translation), and proportional relationships. The construction uses commands such as Rotate, Angle, Polygon, Sequence, Point, Intersect, If, Segment, and Textfield. Key objects include angle variables (angleQ, β, θ), points (P, Q, A, B, C), segments (l1, t1, t2), circles (c, a, b), and interactive text/input boxes. This example is suitable for middle or high school geometry classes, helping students visualize the properties of similar triangles and explore dynamic geometric constructions with sliders and input fields.

GeoGebra Commands & Parameters

  1. Rotate(B - (4, 0), (-(60°)), B) → C
  2. Angle(C, B, A) → β
  3. Polygon(A, B, C) → t1, c, a, b
  4. Sequence(P + ((i * c), 0), i, 0.2, 3, 0.05) → l1
  5. Point(Ray[Rotate[P + (1, 0), ε, P], Rotate[P + (2, 0), ε, P]]) → R1
  6. Intersect(Ray[P, Rotate[P + (1, 0), ε, P]], Ray[Q, Rotate[Q - (1, 0), (-ζ), Q]]) → R_1
  7. Point(Ray[Rotate[Q - (1, 0), (-ζ), Q], Rotate[Q - (2, 0), (-ζ), Q]]) → R2
  8. If(Distance[R1, R_1] < δ, true, false) → close11
  9. If(Distance[R2, R_1] < δ, true, false) → close21
  10. Segment(P, Q) → r
  11. Rotate(Q - (p, 0), (-ζ), Q) → R
  12. Polygon(P, Q, R) → t2, f, g, h
  13. Segment(P, R) → q
  14. Segment(Q, R) → p_2
  15. Angle(R, Q, P) → θ
  16. Textfield(r') → InputBox1
  17. Textfield(p) → InputBox3
  18. Angle(B, A, C) → α
  19. Angle(A, C, B) → γ
  20. Angle(Q, P, R) → η
  21. Angle(P, R, Q) → ι
  22. Segment(P, Q) → i
  23. Textfield(angleQ) → InputBox2