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Law of Cosines Open Middle Problem

Law of Cosines Open Middle Problem
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2020-06-17 04:09
TriangleTrigonometryOptimizationGeometric Construction
This example demonstrates the application of the Law of Cosines in triangles through dynamic interaction, showcasing the relationship between side lengths and angles. Core math concepts include the Law of Cosines, triangle geometry, and optimization problems. Construction highlights involve GeoGebra commands/objects like Intersect, Segment, Circle, Polygon, Angle, Rotate, InteriorAngles, Mode, Length, and If. Suitable for high school mathematics education to deepen students' understanding of the Law of Cosines and develop geometric intuition and problem-solving skills.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Segment(A, B) → j
  3. Segment(B, C) → k
  4. Segment(C, D) → l
  5. Segment(A, E) → m
  6. Segment(E, F) → n
  7. Segment(F, G) → p
  8. Circle(A, m + n + p) → q
  9. Segment(D, H) → r
  10. Segment(H, I) → s
  11. Segment(I, J) → t
  12. Circle(D, r + s + t) → c_1
  13. Intersect(q, c_1, 1) → K
  14. Polygon(A, D, K) → t1, k_1, a_1, d_1
  15. Angle(K, A, G) → α
  16. Angle(J, D, K) → β
  17. Rotate(F, (-α), A) → F'
  18. Rotate(G, (-α), A) → G'
  19. Segment(F', G') → p'
  20. Rotate(E, (-α), A) → E'
  21. Rotate(F, (-α), A) → F'_1
  22. Segment(E', F'_1) → n'
  23. Rotate(A, (-α), A) → A'
  24. Rotate(E, (-α), A) → E'_1
  25. Segment(A', E'_1) → m'
  26. Rotate(I, β, D) → I'
  27. Rotate(J, β, D) → J'
  28. Segment(I', J') → t'
  29. Rotate(H, β, D) → H'
  30. Rotate(I, β, D) → I'_1
  31. Segment(H', I'_1) → s'
  32. Rotate(D, β, D) → D'
  33. Rotate(H, β, D) → H'_1
  34. Segment(D', H'_1) → r'
  35. InteriorAngles(t1) → γ, δ, ε
  36. Mode(l1) → l2
  37. Length(l2) → o
  38. If(o ≟ 0, "No values repeat!", "You have repeated values.") → text1