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Vertical and Adjacent Angles

Vertical and Adjacent Angles
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2016-01-13 21:07
AngleGeometric ConstructionSlider Animation
This example illustrates the concepts of vertical and adjacent angles. Vertical angles are formed by two intersecting lines and are equal, while adjacent angles are formed by the intersection of two lines and sum up to 180 degrees. Using GeoGebra commands such as Segment, Midpoint, Semicircle, Point, Line, Circle, Intersect, and Angle, this dynamic demonstration can be created. Suitable for middle school and above students to learn geometry.

GeoGebra Commands & Parameters

  1. Segment(A, C) → a
  2. Midpoint(a) → O
  3. Semicircle(A, C) → c
  4. Point(c) → D
  5. Line(D, O) → b
  6. Circle(O, D) → d
  7. Intersect(d, b, 2) → B
  8. Segment(D, B) → e
  9. Angle(C, O, D) → α
  10. Angle(D, O, A) → β
  11. Angle(A, O, B) → γ
  12. Angle(B, O, C) → δ
  13. Line(O, xAxis) → f
  14. Point(f) → P
  15. Circle(P, a / 2) → g
  16. Point(g) → E
  17. Segment(E, P) → h
  18. Line(D, f) → i
  19. Intersect(g, i, 1) → D'
  20. Segment(D', P) → j
  21. Line(B, xAxis) → k
  22. Intersect(g, k) → I, B'
  23. Segment(P, B') → l
  24. Point(g) → F
  25. Segment(F, P) → m
  26. Angle(F, P, D') → ε
  27. Angle(D', P, E) → ζ
  28. Angle(E, P, B') → η
  29. Angle(B', P, F) → θ
  30. Point(f) → Q
  31. Point(i) → D''
  32. Point(k) → B''
  33. Segment(D'', B'') → n
  34. Circle(Q, D'') → p
  35. Point(f) → Q_1
  36. Point(p) → H
  37. Segment(Q, H) → q
  38. Angle(B'', Q, H) → ι
  39. Angle(H, Q, D'') → κ
  40. Point(p) → G
  41. Segment(G, Q_1) → r
  42. Angle(D'', Q_1, G) → λ
  43. Angle(G, Q_1, B'') → μ