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Demonstrating Segment Bisectors Definitions

Demonstrating Segment Bisectors Definitions
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2016-05-19 19:21
CircleGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 1) Congruence (Vol 1) Over 80 Resources Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 S N ATTAR CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 Geometry: Introductory Definitions, Postulates, Theorems Congruence: Volume 1 - Chapter 1 Congruence: Volume 1 - Chapter 1
This example engages students in writing definitions for segment bisector, perpendicular line, and perpendicular bisector of a segment by demonstrating their geometric relationships. It involves core concepts like line segment, midpoint, perpendicularity, and circle intersections. Constructed using commands such as Segment, Midpoint, Circle, Intersect, Line, OrthogonalLine, and LineBisector. Suitable for middle school and above, focusing on geometric definitions and constructions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Midpoint(a) → C
  3. Segment(C, B) → b
  4. Circle(C, (0.75 * b)) → c
  5. Intersect(c, a, 2) → D
  6. Intersect(c, a, 1) → E
  7. CircleArc(C, D, E) → d
  8. Point(d) → F
  9. CircleArc(C, D, F) → e
  10. CircleArc(C, F, E) → f
  11. Point(f) → G
  12. CircleArc(C, F, G) → g
  13. CircleArc(C, G, E) → h
  14. Point(h) → H
  15. CircleArc(C, H, E) → k
  16. Point(k) → I
  17. CircleArc(C, I, E) → p
  18. Point(p) → J
  19. Line(F, C) → i
  20. Line(G, C) → j
  21. Line(H, C) → l
  22. Line(I, C) → m
  23. Line(J, C) → n
  24. Segment(A, C) → q
  25. Segment(C, B) → r
  26. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'
  27. Segment(A, A') → s
  28. Dilate(C, If[1 < o ≤ 2, 2 - o, 0], B) → C'
  29. Segment(C, C') → t
  30. Rotate(C, If[2 < o ≤ 3, ((o - 2) * π), 3.141592653589793], C) → C'_1
  31. Rotate(C', If[2 < o ≤ 3, ((o - 2) * π), 3.141592653589793], C) → C''
  32. Segment(C'_1, C'') → t'
  33. Point(a) → K
  34. Point(a) → L
  35. Point(a) → M
  36. Point(a) → N
  37. Point(a) → O
  38. OrthogonalLine(K, a) → a_1
  39. OrthogonalLine(L, a) → b_1
  40. OrthogonalLine(M, a) → c_1
  41. OrthogonalLine(N, a) → d_1
  42. OrthogonalLine(O, a) → e_1
  43. Point(a_1) → P
  44. Point(b_1) → Q
  45. Point(c_1) → R
  46. Point(d_1) → S
  47. Point(e_1) → T
  48. Angle(P, K, A) → α
  49. Angle(Q, L, A) → β
  50. Angle(R, M, A) → γ
  51. Angle(S, N, A) → δ
  52. Angle(T, O, A) → ε
  53. LineBisector(A, B) → f_1
  54. Point(f_1) → U
  55. Angle(U, C, A) → ζ