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Making Similar Triangles by Anthony OR 柯志明 (2)

Making Similar Triangles by Anthony OR 柯志明 (2)
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2019-04-01 09:12
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, and Point, similar triangles can be dynamically constructed. Suitable for students in middle school and above to learn about similar triangles.

GeoGebra Commands & Parameters

  1. Intersect(Circle[A, 4], Circle[B, 6], 1) → C
  2. Polygon(A, B, C) → t1, c, a, b
  3. Textfield(r) → InputBox1
  4. Textfield(p) → InputBox2
  5. Textfield(q) → InputBox3
  6. Intersect(Circle[P, q], Circle[Q, p]) → R_1, R_2, ,
  7. Point(Circle[P, q]) → R1
  8. Point(Circle[Q, p]) → R2
  9. If(Distance[R1, R_1] < δ, true, false) → close11
  10. If(Distance[R1, R_2] < δ, true, false) → close12
  11. If(Distance[R2, R_1] < δ, true, false) → close21
  12. If(Distance[R2, R_2] < δ, true, false) → close22
  13. DynamicCoordinates(R1, If[close11, x(R_1), If[close12, x(R_2), x(R1)]], If[close11, y(R_1), If[close12, y(R_2), y(R1)]]) → R
  14. DynamicCoordinates(R2, If[close21, x(R_1), If[close22, x(R_2), x(R2)]], If[close21, y(R_1), If[close22, y(R_2), y(R2)]]) → R'
  15. Segment(P, Q) → f
  16. Segment(P, R) → g
  17. Segment(Q, R') → h
  18. Polygon(P, Q, R_1) → t2, r_1, p_1, q_1
  19. Polygon(P, Q, R_2) → t3, r_2, p_2, q_2
  20. If(a / p ≟ b / q ≟ c / r, true, false) → proportional
  21. If(proportional ∧ (closed1 ∨ closed2), true, false) → done
  22. Angle(B, A, C) → α
  23. Angle(C, B, A) → β
  24. Angle(A, C, B) → γ
  25. Angle(Q, P, R_1) → ε
  26. Angle(R_1, Q, P) → ζ
  27. Angle(P, R_1, Q) → η
  28. Angle(R_2, P, Q) → θ
  29. Angle(Q, R_2, P) → ι
  30. Angle(P, Q, R_2) → κ

AI Drawing Prompt Reference

Draw two similar triangles generated through transformations. Start by drawing a circle and a square, then find their intersection points to form the first triangle. Next, using two input values, draw circles centered at these points to find the second triangle's vertices. Ensure the triangles are similar, dynamically display their vertices and edges, and measure and show the interior angles to verify similarity.
The prompt above was compiled from the original drawing commands and is for reference only.