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Cosine Rule & Pythagoras' Theorem Demo

Cosine Rule & Pythagoras' Theorem Demo
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2015-04-06 22:13
TriangleTrigonometryGeometric Construction
This example demonstrates the application of the Cosine Rule and Pythagoras' Theorem in calculating side lengths and angles within a triangle. Key math concepts include the Cosine Rule, Pythagorean Theorem, and triangle geometry properties. It is constructed using GeoGebra commands/objects like Segment, Point, Angle, Polygon, OrthogonalLine, Intersect, PointIn, and Length. Suitable for high school mathematics teaching or self-study to understand and apply trigonometric functions and geometric theorems.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Point(c_3) → C_1
  3. Segment(C_1, A) → b
  4. Angle(C_1, A, B) → C
  5. Segment(C_1, B) → c
  6. Polygon(A, E, D, B) → poly1, a_1, e, d_1, b_1
  7. OrthogonalLine(C_1, b) → i
  8. OrthogonalLine(A, b) → j
  9. Intersect(c_3, j) → F, G
  10. OrthogonalLine(F, j) → f
  11. Intersect(i, f) → H
  12. Polygon(H, F, A, C_1) → poly2, h, f_2, a_2, c_1
  13. PointIn(poly2) → Pointpoly2
  14. OrthogonalLine(C_1, c) → g
  15. OrthogonalLine(B, c) → k
  16. Length(c) → l
  17. Intersect(p, k) → I, J
  18. OrthogonalLine(J, k) → m
  19. Intersect(g, m) → K
  20. Polygon(K, C_1, B, J) → poly3, k_1, c_2, b_2, j_1
  21. PointIn(poly3) → Pointpoly3
  22. PointIn(poly1) → Pointpoly1
  23. Segment(A_1, B_1) → a_3
  24. Point(c_4) → C_2
  25. Segment(C_2, A_1) → b_3
  26. Angle(C_2, A_1, B_1) → C_3
  27. Segment(C_2, B_1) → c_5
  28. OrthogonalLine(C_2, c_5) → g_1
  29. OrthogonalLine(B_1, c_5) → k_2
  30. Length(c_5) → l_1
  31. Point(c_6) → C_4
  32. Segment(C_4, B_2) → c_7
  33. OrthogonalLine(C_4, c_7) → g_2
  34. OrthogonalLine(B_2, c_7) → k_3
  35. Length(c_7) → l_2
  36. Segment(A_2, B_3) → a_4
  37. Point(c_8) → C_5
  38. Segment(C_5, A_2) → b_4
  39. Angle(C_5, A_2, B_3) → C_6
  40. Segment(C_5, B_3) → c_9