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Angle Bisector Construction Demonstration

Angle Bisector Construction Demonstration
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2017-02-17 17:52
CircleAngleGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 Construction Constructions (Dynamic Illustrations)
This example dynamically demonstrates the construction of an angle bisector using compass and straightedge. Key concepts include angle bisectors, circles, and intersections. GeoGebra commands used include Ray, Rotate, Angle, Circle, Intersect, etc. Suitable for middle school and above students learning geometric constructions.

GeoGebra Commands & Parameters

  1. Ray(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Circle(A, b) → c
  6. Rotate(B, (a / 2 * π / 180), A) → B'_1
  7. Angle(B, A, B'_1) → β
  8. Ray(A, B'_1) → h
  9. Intersect(c, f, 1) → C
  10. Intersect(c, g) → D,
  11. OrthogonalLine(C, h) → i
  12. Intersect(i, h) → E
  13. Distance(C, E) → d
  14. Circle(C, e) → k
  15. Circle(D, e) → p
  16. Intersect(k, p, 2) → F
  17. Rotate(C, If[1 < j ≤ 2, (((j - 1) * 2) * π), (2 * π)], A) → C'
  18. CircleArc(A, C, C') → q
  19. Intersect(k, f, 1) → G
  20. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], C) → A'
  21. Segment(A, A') → l
  22. Dilate(C, If[2 < j ≤ 3, 3 - j, 0], G) → C'_1
  23. Segment(C, C'_1) → m
  24. Rotate(G, If[3 < j ≤ 4, (((j - 3) * 2) * π), (2 * π)], C) → G'
  25. CircleArc(C, G, G') → r
  26. Dilate(C, If[4 < j ≤ 5, 5 - j, 0], D) → C'_2
  27. Vector(C, C'_2) → u
  28. Translate(C, u) → C'_3
  29. Translate(C'_1, u) → H
  30. Segment(C'_3, H) → m'
  31. Rotate(H, If[5 < j ≤ 6, (((j - 5) * 2) * π), (2 * π)], D) → H'
  32. CircleArc(D, H, H') → s
  33. Angle(H, D, F) → γ
  34. Angle(H, D, H') → δ
  35. Circle(F, 2) → t
  36. Intersect(t, h, 2) → I
  37. Circle(A, (0.3 * b)) → c_1
  38. Intersect(c_1, h, 1) → J
  39. Intersect(f, l) → K
  40. Intersect(c_1, f) → L,
  41. CircleSector(A, L, J) → d_1
  42. Ray(F, I) → n
  43. Dilate(A, If[6 < j ≤ 7, 7 - j, 0], F) → A'_1
  44. Segment(A, A'_1) → f_1
  45. Rotate(L, If[7 < j ≤ 8, (((j - 7) * a / 2) * π / 180), (a / 2 * π / 180)], A) → L'
  46. CircleSector(A, L, L') → e_1
  47. Rotate(e_1, If[9 < j ≤ 10, (((j - 9) * a / 2) * π / 180), (a / 2 * π / 180)], A) → g_1