MathPlotAI Logo MathPlotAI

Proof of the Law of Cosines

Proof of the Law of Cosines
Loading the math board and drawing, please wait…
2015-12-14 14:48
TriangleTrigonometryGeometric Construction
This example demonstrates the proof of the Law of Cosines, which describes the relationship between the sides and angles of a triangle. Using GeoGebra commands such as Line, Intersect, Segment, the construction shows how to geometrically prove the Law of Cosines. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, C) → a_1
  2. OrthogonalLine(B, a_1) → d
  3. Intersect(a_1, d) → D
  4. Segment(A, D) → b_1
  5. Segment(A, C) → b
  6. Segment(C, B) → a
  7. Segment(B, D) → f
  8. Segment(B, A) → c
  9. Angle(C, D, B) → α
  10. Angle(C, A, B) → β
  11. Angle(B, A, D) → θ
  12. Angle(B, C, A) → γ
  13. Segment(C, D) → e
  14. Angle(A, C, B) → δ
  15. Angle(A, B, C) → ε