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Pythagorean Theorem and Law of Cosines Demo

Pythagorean Theorem and Law of Cosines Demo
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2019-09-16 23:22
TriangleTrigonometryGeometric Construction
This example demonstrates the application of the Pythagorean Theorem and the Law of Cosines in triangles. Key math concepts include the Pythagorean Theorem, Law of Cosines, and triangle geometry properties. Construction involves commands like Point, Segment, Polygon, and Angle in GeoGebra. Suitable for high school mathematics teaching or geometry learning, helping to understand the relationship between trigonometric functions and geometric figures.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Point(e_1) → C
  3. Segment(C, B) → c_3
  4. Segment(A, B) → a_3
  5. Segment(A, C) → b_3
  6. Point(xAxis) → D
  7. Point(xAxis) → E
  8. Point(xAxis) → F
  9. Point(xAxis) → G
  10. Segment(D, E) → i
  11. Segment(F, G) → j
  12. Point(xAxis) → L
  13. Point(xAxis) → M
  14. Point(xAxis) → N
  15. Point(xAxis) → O
  16. Segment(L, M) → k
  17. Segment(N, O) → l
  18. Polygon(D, E, I, H) → q1, d, e, i_1, h
  19. Polygon(J, K, G, F) → q2, j_1, k_1, g, f
  20. Polygon(P, Q, M, L) → q3, p, q, m, l_1
  21. Polygon(R, S, Q, P) → q4, r, s, q_1, p_1
  22. Polygon(T, U, O, N) → q5, t, u, o, n
  23. Polygon(B, A, 4) → b_4, f_1, g_1, h_1, m_1, V, W
  24. Polygon(A, C, 4) → a_4, n_1, r_1, s_1, t_1, Z, A_1
  25. Polygon(C, B, 4) → c_4, a_1, b_1, c_1, d_1, B_1, C_1
  26. Polygon(A, B, C) → t1, c_2, a_2, b_2
  27. Segment(C, A) → b
  28. Segment(A, B) → a
  29. Segment(B, C) → c
  30. Angle(B, A, C) → α