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Pythagorean Theorem Generalization on Polygons

Pythagorean Theorem Generalization on Polygons
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2018-04-03 21:24
PolygonVectorGeometric Construction
This example demonstrates the generalization of the Pythagorean theorem on polygons. By constructing regular polygons, observe the relationships between their sides and diagonals. Commands used include Midpoint, Circle, Polygon, LineBisector, etc. Suitable for middle school and above students to learn geometric transformations and polygon properties.

GeoGebra Commands & Parameters

  1. Midpoint(B, A) → M_c
  2. Circle(M_c, B) → c_1
  3. Point(c_1) → C
  4. Polygon(B, A, C) → righttriangle, c, a, b
  5. Polygon(A, B, n) → polyc, d_1, J, M, P, a_1, g, j, m, r, b_1, D, G
  6. Polygon(B, C, n) → polya, e_1, K, N, Q, b_2, h, k, p, s, g_1, E, H
  7. Polygon(C, A, n) → polyb, f_1, L, O, R, c_3, i, l, q, t, h_1, F, I
  8. LineBisector(c) → d
  9. LineBisector(a) → e
  10. LineBisector(b) → f
  11. Angle(B, C, A) → α
  12. Rotate(B, 90° - (180 * ° / n), A) → B'
  13. Line(A, B') → i_1
  14. Intersect(d, i_1) → O_c
  15. Rotate(A, 90° - (180 * ° / n), C) → A'
  16. Line(C, A') → j_1
  17. Intersect(e, j_1) → O_b
  18. Rotate(C, 90° - (180 * ° / n), B) → C'
  19. Line(B, C') → k_1
  20. Intersect(f, k_1) → O_a
  21. Segment(A, O_c) → l_1
  22. Segment(B, O_c) → m_1
  23. Segment(M_c, O_c) → n_1
  24. Angle(M_c, O_c, B) → β
  25. Segment(A, O_b) → p_1
  26. Segment(C, O_b) → q_1
  27. Midpoint(C, A) → M_b
  28. Segment(M_b, O_b) → r_1
  29. Angle(C, O_b, M_b) → γ
  30. Segment(C, O_a) → s_1
  31. Segment(B, O_a) → t_1
  32. Midpoint(B, C) → M_a
  33. Segment(M_a, O_a) → a_2
  34. Angle(B, O_a, M_a) → δ