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Constructing Square Roots Method 1

Constructing Square Roots Method 1
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2015-12-16 23:01
TriangleCircleGeometric Construction
This example demonstrates the geometric method for constructing square roots. It involves core mathematical concepts such as right triangles, circles, similar triangles, and the Pythagorean theorem. Key GeoGebra commands and objects used in the construction include Segment, Vector, Translate, OrthogonalLine, Circle, Intersect, and Angle. Suitable for middle school students and above to learn and understand the geometric meaning of square roots, as well as for math competition or enrichment purposes.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Vector(A, B) → u
  3. Translate(C, u) → C'
  4. Segment(C, C') → b
  5. OrthogonalLine(C', b) → c
  6. Circle(C', C) → d
  7. Intersect(d, c, 2) → D
  8. Segment(C, D) → e
  9. OrthogonalLine(D, e) → f
  10. Circle(D, a) → g
  11. Intersect(g, f, 2) → E
  12. Segment(E, C) → h
  13. OrthogonalLine(E, h) → i
  14. Circle(E, a) → k
  15. Intersect(k, i, 1) → F
  16. Segment(F, C) → j
  17. Segment(F, E) → l
  18. Segment(E, D) → m
  19. Segment(D, C') → n
  20. OrthogonalLine(F, j) → p
  21. Circle(F, a) → q
  22. Intersect(q, p, 1) → G
  23. Segment(G, C) → r
  24. Segment(G, F) → s
  25. OrthogonalLine(G, r) → t
  26. Circle(G, a) → c_1
  27. Intersect(c_1, t, 1) → H
  28. Segment(H, G) → a_1
  29. Segment(H, C) → b_1
  30. Angle(D, C', C) → α
  31. Angle(E, D, C) → β
  32. Angle(F, E, C) → γ
  33. Angle(G, F, C) → δ
  34. Angle(H, G, C) → ε