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Pythagoras with Pentagons

Pythagoras with Pentagons
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2017-01-05 00:43
TrianglePolygonOptimizationGeometric Construction
This example demonstrates constructing right triangles within a pentagon and verifying the Pythagorean theorem. Key math concepts include the Pythagorean theorem, right triangles, and polygonal geometry. GeoGebra commands used are Intersect, Angle, Segment, and Polygon for construction. Suitable for high school mathematics education or exploration by math enthusiasts.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Angle(A, B, C) → α
  3. Segment(A, B) → s
  4. Segment(B, C) → t
  5. Segment(C, A) → c
  6. Polygon(A, C, 5) → Area_C, r_1, s_1, t_1, a_1, b_1, T, U, V
  7. Polygon(C, B, 5) → Area_B, q_1, d_1, e_1, f_2, g_2, Z, A_1, B_1
  8. Polygon(B, A, 5) → Area_A, k_1, l_1, m_1, n_1, p_1, D_1, E_1, F_1
  9. Polygon(B, A, 5) → poly1, f, g, h, i, j, D, E, H
  10. Polygon(C, B, 5) → poly2, k, l, m, n, p, I, L, M
  11. Polygon(A, C, 5) → poly3, q, r, e, f_1, g_1, N, O, P