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Pythagorean Theorem Puzzle

Pythagorean Theorem Puzzle
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2017-09-23 10:49
TrianglePolygonSolid GeometryComplex NumberGeometric Construction
In collections Pythagoras
This example dynamically demonstrates the Pythagorean theorem by showing the relationship between the sides of a right triangle. It involves core math concepts like right triangles, the Pythagorean theorem, polygon construction, and complex numbers. Construction highlights include using Point and Polygon commands to create points A, B, C and shapes like poly1, poly2, with operations such as Subtraction and Complex Numbers. Suitable for middle school students learning geometric constructions and theorem verification, or high schoolers exploring solid geometry initially.

GeoGebra Commands & Parameters

  1. Point(Circle[A, 2]) → B
  2. Polygon(A, B, C) → poly1, c, a, b
  3. Point(Circle[D, 2]) → E
  4. Polygon(D, E, F) → poly2, f, d, e
  5. Point(Circle[G, 2]) → H
  6. Polygon(G, H, I) → poly3, i, g, h
  7. Point(Circle[J, 2]) → K
  8. Polygon(J, K, L) → poly4, l, j, k
  9. Polygon(M, N, 4) → poly5, q, r, s, t, O, P
  10. Point(Circle[Q, 3.605551275463989]) → R
  11. Polygon(Q, R, S, T) → poly6, q_1, r_1, s_1, t_1
  12. Polygon(U, V, 4) → poly7, f_1, g_1, h_1, i_1, W, Z
  13. Polygon(A_1, B_1, 4) → poly8, j_1, k_1, l_1, m_1, C_1, D_1
  14. Polygon(E_1, F_1, 4) → poly9, n_1, p_1, a_1, b_1, G_1, H_1