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Proofs of Sine, Cosine Rules, and Triangle Area by Mr Hardman

Proofs of Sine, Cosine Rules, and Triangle Area by Mr Hardman
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2015-07-22 17:17
TriangleTrigonometryGeometric Construction
This example dynamically demonstrates proofs of the Sine Rule, Cosine Rule, and Triangle Area Formula. It involves core math concepts like trigonometric functions, geometric constructions, and triangle side-angle relationships. Constructed using commands like Line, Segment, OrthogonalLine, Intersect, Polygon, Angle, Vector, it is suitable for GCSE, IGCSE, A-Level (Edexcel C2) students and teachers.

GeoGebra Commands & Parameters

  1. Line(A, C) → a
  2. Segment(B, A) → b
  3. Segment(B, C) → c
  4. Segment(C, A) → d
  5. OrthogonalLine(B, a) → e
  6. Intersect(a, e) → D
  7. Segment(B, D) → f
  8. Segment(D, A) → g
  9. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  10. Angle(B, D, C) → α
  11. Angle(A, D, B) → β
  12. Angle(D, A, B) → γ
  13. Angle(B, C, D) → δ
  14. Segment(D, A) → j
  15. Segment(D, C) → k
  16. Vector(E, F) → u
  17. Vector(G, H) → v