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Making Similar Triangles by Anthony OR 柯志明

Making Similar Triangles by Anthony OR 柯志明
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2019-04-07 22:15
TriangleGeometric Construction
In collections Making Similar Triangles
This example demonstrates how to generate similar triangles through transformations. Key mathematical concepts include the properties of similar triangles and similarity transformations. Using GeoGebra commands such as Intersect, Polygon, Sequence, etc., the construction process of similar triangles is dynamically illustrated. Suitable for students at the junior high school level and above to learn about similar triangles.

GeoGebra Commands & Parameters

  1. Intersect(Line[A, Rotate[A + (1, 0), 45°, A]], Line[B, Rotate[B - (1, 0), (-(23°)), B]]) → C
  2. Polygon(A, B, C) → t1, c, a, b
  3. Sequence(P + ((i * c), 0), i, 0.2, 3, 0.05) → l1
  4. Angle(C, B, A) → β
  5. Point(l1) → Q
  6. Angle(B, A, C) → α
  7. Point(Ray[Rotate[P + (1, 0), ε, P], Rotate[P + (2, 0), ε, P]]) → R1
  8. Intersect(Ray[P, Rotate[P + (1, 0), ε, P]], Ray[Q, Rotate[Q - (1, 0), (-ζ), Q]]) → R_1
  9. Point(Ray[Rotate[Q - (1, 0), (-ζ), Q], Rotate[Q - (2, 0), (-ζ), Q]]) → R2
  10. If(Distance[R1, R_1] < δ, true, false) → close11
  11. If(Distance[R2, R_1] < δ, true, false) → close21
  12. Segment(P, Q) → r
  13. Polygon(P, Q, R_1) → t2, r_1, p_1, q_1
  14. Angle(A, C, B) → γ
  15. DynamicCoordinates(R1, If[Distance[R1, R_1] < δ, x(R_1), x(R1)], If[Distance[R1, R_1] < δ, y(R_1), y(R1)]) → R
  16. DynamicCoordinates(R2, If[Distance[R2, R_1] < δ, x(R_1), x(R2)], If[Distance[R2, R_1] < δ, y(R_1), y(R2)]) → R'
  17. Segment(P, R) → q
  18. Segment(Q, R') → p
  19. Angle(Q, P, R) → η
  20. Angle(R', Q, P) → θ
  21. If(α ≟ ε ∧ β ≟ ζ, true, false) → AAA
  22. Angle(P, R, Q) → ι
  23. Textfield(angleP) → InputBox1
  24. Textfield(angleQ) → InputBox2