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Law of Cosine Proof

Law of Cosine Proof
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2015-11-11 08:38
TriangleTrigonometryGeometric Construction
This example dynamically demonstrates the proof of the Law of Cosines for any triangle. Key math concepts include the Law of Cosines, trigonometry, and geometric construction. It uses commands like Point, Segment, OrthogonalLine, Intersect, Angle, Polygon to build the triangle and auxiliary lines, illustrating the theorem's derivation. Suitable for high school mathematics instruction and student exploration.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → C
  3. Segment(A, C) → b
  4. Segment(C, B) → a
  5. Segment(B, A) → c
  6. OrthogonalLine(B, xAxis) → d
  7. Intersect(d, b) → D
  8. Segment(A, D) → k
  9. Segment(D, C) → f
  10. Segment(D, B) → h
  11. OrthogonalLine(A, a) → h_1
  12. OrthogonalLine(B, h_1) → i
  13. Intersect(h_1, i) → E
  14. Segment(E, B) → j
  15. Angle(B, D, A) → β
  16. Polygon(A, D, B) → poly1, b_1, a_1, d_1
  17. Polygon(B, D, C) → poly2, e, m, n