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Pythagoras and Cosine Rule with Scale Factors

Pythagoras and Cosine Rule with Scale Factors
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2019-10-17 22:08
TriangleTrigonometryGeometric Construction
This example demonstrates the Pythagorean theorem and the cosine rule using scale factors. It involves trigonometry and geometric construction. By using commands like Polygon, Line, Circle, Intersect, Segment, OrthogonalLine, Angle, multiple triangles are constructed and the application of the theorems is observed by adjusting the scale factors. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Line(D, xAxis) → f
  3. Circle(D, (c * c)) → d
  4. Intersect(d, f, 2) → E
  5. Circle(E, (a * c)) → g
  6. Circle(D, (b * c)) → e
  7. Intersect(g, e, 2) → F
  8. Segment(E, F) → h
  9. Segment(D, F) → i
  10. Segment(D, E) → j
  11. Circle(F, (b * b)) → k
  12. Circle(D, (a * b)) → p
  13. Intersect(k, p, 2) → G
  14. Segment(D, G) → l
  15. Segment(G, F) → m
  16. Circle(F, (a * a)) → q
  17. Circle(E, (a * b)) → r
  18. Intersect(q, r, 1) → H
  19. Segment(F, H) → n
  20. Segment(H, E) → s
  21. Line(C, xAxis) → t
  22. OrthogonalLine(C, xAxis) → f_1
  23. Angle(A, C, B) → α
  24. Angle(D, G, F) → β
  25. Angle(D, F, E) → γ
  26. Angle(F, H, E) → δ
  27. Angle(B, A, C) → ε
  28. Angle(G, F, D) → ζ
  29. Angle(E, D, F) → η
  30. Angle(H, E, F) → θ
  31. Angle(C, B, A) → ι
  32. Angle(F, D, G) → κ
  33. Angle(F, E, D) → λ
  34. Angle(E, F, H) → μ

AI Drawing Prompt Reference

Draw an arbitrary triangle and a horizontal baseline. Using one vertex as center, draw a circle with radius equal to the square of a side length, intersecting the baseline at a new point. Then, using this new point and another vertex as centers, draw circles with radii equal to products of side lengths; their intersection forms another triangle. Repeat this process to construct several similar triangles, labeling all interior angles. By adjusting scale factors, observe the geometric relationships of the Pythagorean theorem and the cosine rule.
The prompt above was compiled from the original drawing commands and is for reference only.