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Proofs of Sine, Cosine Rules, and Triangle Area

Proofs of Sine, Cosine Rules, and Triangle Area
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2016-11-30 19:10
TriangleTrigonometryGeometric Construction
This example dynamically demonstrates proofs of the sine rule, cosine rule, and area formula for a triangle. It involves core math concepts like trigonometric functions, geometric constructions, and vector operations. Constructed using GeoGebra commands such as Line, Segment, OrthogonalLine, Intersect, Polygon, Angle, Vector. Suitable for high school mathematics teaching and geometric proof learning.

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