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Constructing Congruent Angles by Tim Brzezinski

Constructing Congruent Angles by Tim Brzezinski
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2017-02-17 03:24
CircleAngleGeometric Construction
This example demonstrates how to construct an angle congruent to a given angle using compass and straightedge. It involves core mathematical concepts such as angles, circles, congruence, and geometric construction. Key GeoGebra commands used include Ray, Rotate, Angle, Point, Circle, Intersect, CircleArc, Dilate, Vector, Translate, Segment, Distance, CircleSector, and Line. Suitable for middle school and above learning geometric constructions and congruence theorems.

GeoGebra Commands & Parameters

  1. Ray(A, B) → f
  2. Rotate(B, (o * π / 180), A) → B'
  3. Angle(B, A, B') → β
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Circle(A, C) → c
  7. Intersect(c, f, 1) → D
  8. Rotate(D, If[0 < a ≤ 1, ((a * 2) * π), (2 * π)], A) → D'
  9. Rotate(C, If[0 < a ≤ 1, (((-a) * 2) * π), (-2 * π)], A) → C'
  10. CircleArc(A, C', C) → d
  11. Ray(E, F) → h
  12. Dilate(A, If[1 < a ≤ 2, 2 - a, 0], E) → A'
  13. Vector(A, A') → u
  14. Translate(c, u) → c'
  15. Translate(A, u) → A'_1
  16. Intersect(c', h, 1) → G
  17. Circle(C, D) → e
  18. Rotate(D, If[2 < a ≤ 3, (((-(a - 2)) * 2) * π), (-2 * π)], C) → C'_1
  19. CircleArc(C, C'_1, D) → k
  20. Dilate(C, If[3 < a ≤ 4, 4 - a, 0], G) → C'_2
  21. Vector(C, C'_2) → v
  22. Translate(e, v) → e'
  23. Translate(C, v) → C'_3
  24. Intersect(e', c') → H, I, ,
  25. Dilate(E, If[5 < a ≤ 6, 6 - a, 0], I) → E'
  26. Vector(E, E') → w
  27. Segment(E, E') → i
  28. Ray(E, I) → j
  29. Circle(I, 5) → p
  30. Intersect(p, j, 2) → J
  31. Distance(A, C) → b
  32. Circle(A, (0.5 * b)) → q
  33. Intersect(q, f, 1) → K
  34. Rotate(K, If[6.5 < a ≤ 7.5, (((a - 6.5) * o) * π / 180), (o * π / 180)], A) → K'
  35. CircleSector(A, K, K') → r
  36. Dilate(A, If[8 < a ≤ 9, 9 - a, 0], E) → A'_2
  37. Vector(A, A'_2) → m
  38. Translate(r, m) → r'
  39. Line(E, f) → n
  40. Line(E, g) → s
  41. Point(s) → L
  42. Point(n) → M
  43. Angle(L, E, I) → γ
  44. Rotate(r', If[9 < a ≤ 10, ((a - 9) * γ), γ], E) → r''
  45. Ray(E, I) → l
  46. Intersect(p, l, 2) → N
  47. Ray(I, N) → t