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Cosine Theorem and Triangle Reflection Animation

Cosine Theorem and Triangle Reflection Animation
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2016-07-09 12:12
TrigonometryGeometric Construction
In collections Geometry Review Similarity, Right Triangles, and Trigonometry (SRT) Cluster
This example demonstrates the application of the cosine theorem in right triangles and reflection phenomena through animation. It involves core math concepts like the cosine theorem, right triangles, reflection, angles, expected value, cones, and hyperbolas. Construction highlights include commands like Segment, OrthogonalLine, Point, Ray, Angle, Rotate, Polygon, Midpoint, and Vector in GeoGebra. Suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → E
  4. Ray(B, E) → c
  5. Angle(A, B, E) → α
  6. Point(c) → C
  7. Segment(C, A) → d
  8. Angle(B, C, A) → β
  9. Segment(B, C) → e
  10. Rotate(B, If[0 < f ≤ 1, (f * β), β], C) → B'
  11. Rotate(C, If[0 < f ≤ 1, (f * β), 0], C) → C'
  12. Segment(B', C') → e'
  13. Angle(C, A, B) → γ
  14. Rotate(A, If[0 < g ≤ 1, ((-g) * γ), 0], A) → A'
  15. Rotate(B, If[0 < g ≤ 1, ((-g) * γ), (-γ)], A) → B'_1
  16. Segment(A', B'_1) → a'
  17. Rotate(B, If[0 < h ≤ 1, ((-h) * α), 0], B) → B'_2
  18. Rotate(C, If[0 < h ≤ 1, ((-h) * α), 0], B) → C'_1
  19. Segment(B'_2, C'_1) → e'_1
  20. Polygon(B, A, C) → poly1, c_1, b_1, a_1
  21. Midpoint(e') → D
  22. Vector(F, D) → u
  23. Midpoint(a') → G
  24. Vector(H, G) → v
  25. Midpoint(e'_1) → I
  26. Vector(J, I) → w
  27. Ray(B, A) → j