MathPlotAI Logo MathPlotAI

Law of Cosines Demonstration by David Cowan

Law of Cosines Demonstration by David Cowan
Loading the math board and drawing, please wait…
2015-02-09 03:25
TriangleTrigonometryGeometric Construction
This example demonstrates the Law of Cosines in triangle geometry, illustrating the relationship between side lengths and angles dynamically. Key math concepts include the Law of Cosines, triangle properties, and linear equations. Construction involves commands/objects like Point, Polygon, OrthogonalLine, Intersect, PointIn, Segment. Suitable for high school mathematics teaching, aiding students in visualizing the proof and application of the Law of Cosines.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Polygon(B, A, C) → poly1, b, c, a
  3. OrthogonalLine(C, b) → d
  4. OrthogonalLine(B, c) → e
  5. OrthogonalLine(A, a) → f
  6. Polygon(C, B, 4) → poly2, g, h, i, j, D, E
  7. Polygon(F, C, 4) → poly3, k, l, m, n, G, H
  8. Polygon(B, F, 4) → poly4, p, q, r, s, I, J
  9. Intersect(f, a) → K
  10. Intersect(e, c) → L
  11. Intersect(d, b) → M
  12. Intersect(f, i) → N
  13. Intersect(e, m) → O
  14. Intersect(d, r) → P
  15. Polygon(K, N, E, C) → poly5, k_1, n_1, e_1, b_1
  16. Polygon(C, L, O, G) → poly6, b_2, l_1, o, g_1
  17. PointIn(poly5) → Pointpoly5
  18. PointIn(poly6) → Pointpoly6
  19. Polygon(N, D, B, K) → poly7, n_2, d_1, c_1, k_2
  20. Polygon(B, J, P, M) → poly8, c_2, j_1, p_1, m_1
  21. PointIn(poly7) → Pointpoly7
  22. PointIn(poly8) → Pointpoly8
  23. Polygon(F, M, P, I) → poly9, f_1, m_2, p_2, i_1
  24. Polygon(F, L, O, H) → poly10, f_2, l_2, o_1, h_1
  25. PointIn(poly10) → Pointpoly10
  26. PointIn(poly9) → Pointpoly9
  27. Segment(L, B) → s_1
  28. Segment(F, K) → t_1
  29. Segment(M, C) → a_2
  30. Segment(L, O) → a_1
  31. Segment(K, N) → q_1
  32. Segment(M, P) → r_1
  33. Polygon(C, L, B) → poly11, b_3, c_3, l_3
  34. Polygon(C, K, F) → poly12, f_3, c_4, k_3
  35. Polygon(L, B, F) → poly13, f_4, l_4, b_4

AI Drawing Prompt Reference

Draw a triangle ABC with points A, B, and C on the x-axis. Construct perpendicular lines from point C to AB, from point B to AC, and from point A to BC. Form a quadrilateral by connecting the vertices of the triangle with their respective feet of the perpendiculars, creating several intersection points and segments. Use these points and segments to construct multiple triangles and quadrilaterals, illustrating the relationship between side lengths and angles in a triangle, as well as the properties of the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.