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Construct Similar Triangles (SSS)

Construct Similar Triangles (SSS)
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2020-12-01 22:20
TriangleTransformationGeometric Construction
This example demonstrates how to construct similar triangles using the SSS (Side-Side-Side) condition. Key mathematical concepts include the properties of similar triangles and similarity transformations. It utilizes commands such as Intersect, Polygon, Textfield, Point, If, DynamicCoordinates, Segment, and Angle in GeoGebra. Suitable for middle school and above students 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 triangles, one fixed and one adjustable similar triangle. Start with a fixed triangle whose vertices are determined by the intersection of two circles with radii 4 and 6. Then place two movable points on circles to adjust the shape of the similar triangle. Use three input boxes to control the side length ratios. Connect the points to form the second triangle and display its three interior angles. When the corresponding sides are proportional and vertices coincide, show a completion message. Also label all angles and indicate whether the triangles are similar.
The prompt above was compiled from the original drawing commands and is for reference only.