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Differentiation Example: Discovering the Vertical Angles Theorem

Differentiation Example: Discovering the Vertical Angles Theorem
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2018-01-02 05:49
AngleCalculusDerivative
This is a teacher example that demonstrates differentiation conceptually to students, helping them discover the vertical angles theorem. It uses commands such as Point, Line, Rotate, Angle, Circle, Intersect, Segment, CircleSector, Ray, CircleArc, etc. Suitable for high school mathematics, particularly in coordinate geometry and calculus courses.

GeoGebra Commands & Parameters

  1. Point(y = 0) → A
  2. Line(A, B) → f
  3. Rotate(B, α, A) → B'
  4. Angle(B, A, B') → γ
  5. Line(A, B') → g
  6. Rotate(B', β, A) → B''
  7. Angle(B', A, B'') → δ
  8. Line(A, B'') → h
  9. Circle(A, a) → c
  10. Intersect(c, h, 2) → C
  11. Circle(C, A) → d
  12. Circle(A, C) → e
  13. Intersect(e, h, 2) → J
  14. Segment(A, C) → j
  15. Circle(A, (0.3 * j)) → k
  16. Circle(C, (0.3 * j)) → p
  17. Intersect(p, h) → N, O
  18. Intersect(k, h) → P, Q
  19. Intersect(k, g) → T, U
  20. CircleSector(A, U, Q) → q
  21. Circle(C, j / 2) → g_1
  22. Circle(A, j / 2) → h_1
  23. Intersect(g_1, h, 2) → H
  24. Intersect(g_1, h) → I, Z
  25. Intersect(h_1, h) → A_1, B_1
  26. Intersect(h_1, g) → E_1, F_1
  27. Ray(A, A_1) → m
  28. Ray(C, H) → n
  29. CircleArc(C, N, O) → r
  30. Segment(A, C) → b
  31. CircleArc(A, T, U) → s
  32. Point(s) → D
  33. Rotate(D, β, A) → D'
  34. Angle(D, A, D') → ε
  35. CircleSector(A, D, D') → t
  36. Line(P, Q) → i