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Cosine & Pythagorean Theorems Demo

Cosine & Pythagorean Theorems Demo
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2018-12-27 05:37
TriangleTrigonometryGeometric Construction
This example demonstrates the application and verification of the Cosine Rule and Pythagorean Theorem in triangles. It involves core math concepts like the Cosine Rule, Pythagorean Theorem, and relationships between triangle sides and angles. Construction highlights include commands/objects like Segment, Point, Angle, Polygon, OrthogonalLine, Intersect, PointIn, and Length from GeoGebra. Suitable for high school mathematics teaching or student exploration of triangle geometry.

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