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Cosine Theorem Demonstration

Cosine Theorem Demonstration
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2016-08-26 04:01
TriangleTrigonometryGeometric Construction
This example dynamically demonstrates the relationship between the sides and an angle of a triangle, visually showcasing the application of the Cosine Theorem. It involves core mathematical concepts such as the Cosine Theorem, triangle geometry, vectors, and functions. The construction uses GeoGebra commands like Point, Segment, Angle, Polygon, and defines objects like a_2, b_1, A, B, c, C, α_3, β, γ, etc., with slider animations to illustrate variations. It is suitable for high school mathematics teaching to help students understand the Cosine Theorem and its application in solving triangles.

GeoGebra Commands & Parameters

  1. Point(Circle[A, a_2]) → B
  2. Segment(A, B) → c
  3. Point(Circle[A, b_1]) → C
  4. Segment(A, C) → b
  5. Segment(C, B) → a
  6. Angle(B, A, C) → α_3
  7. Angle(A, C, B) → β
  8. Angle(C, B, A) → γ
  9. Polygon(A, C, B) → poly1, b_2, a_1, c_1
  10. Point(Circle[A_1, a_2]) → B_1
  11. Segment(A_1, B_1) → c_2
  12. Point(Circle[A_1, b_1]) → C_1
  13. Segment(A_1, C_1) → b_3
  14. Segment(C_1, B_1) → a_3
  15. Angle(B_1, A_1, C_1) → α_1
  16. Angle(A_1, C_1, B_1) → β_1
  17. Angle(C_1, B_1, A_1) → γ_1
  18. Polygon(A_1, C_1, B_1) → poly1_1, b_4, a_4, c_3
  19. Point(Circle[A_2, a_5]) → B_2
  20. Segment(A_2, B_2) → c_4
  21. Point(Circle[A_2, b_5]) → C_2
  22. Segment(A_2, C_2) → b_6
  23. Segment(C_2, B_2) → a_6
  24. Angle(B_2, A_2, C_2) → α_2
  25. Angle(A_2, C_2, B_2) → β_2
  26. Angle(C_2, B_2, A_2) → γ_2
  27. Polygon(A_2, C_2, B_2) → poly1_2, b_7, a_7, c_5

AI Drawing Prompt Reference

Draw a triangle ABC with vertices A, B, and C, and sides a, b, and c, and angles α, β, and γ. Use circle and point construction methods to create three similar triangles A_1B_1C_1, A_2B_2C_2, and demonstrate changes in angles and side lengths by adjusting sliders.
The prompt above was compiled from the original drawing commands and is for reference only.