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Pythagoras' Theorem (3 Polygons)

Pythagoras' Theorem (3 Polygons)
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2020-07-09 10:19
TrianglePolygonGeometric Construction
This example demonstrates the proof of Pythagoras' Theorem using three polygons to illustrate the relationship between the sides of a right triangle. Core math concepts include Pythagorean Theorem, polygon construction, and coordinate geometry. It is constructed using GeoGebra commands like Segment, OrthogonalLine, Point, Polygon, Intersect, and Angle, making it suitable for high school mathematics education and understanding geometric proofs.

GeoGebra Commands & Parameters

  1. Segment(A_2, B_2) → a
  2. OrthogonalLine(A_2, a) → b
  3. Point(b) → C_2
  4. Polygon(C_2, B_2, A_2) → poly1, a_1, c, b_1
  5. Polygon(C_2, B_2, n) → C, d, p_1, s_1, g_2, j_2, k_2, q_2, t_2, c_2, f_3, i_3, e, l_3, p_3, s_3, b_3, e_3, h_4, k_4, n_4, r_4, a_4, f, d_4, D, E, F, G, H, S, V, A_1, D_1, g, G_1, J_1, K_1, P_1, S_1, V_1, D_2, G_2, J_2, M_2, h, P_2, S_2, V_2, A_3, D_3, G_3, J_3, M_3, P_3, i, j, i_1, l_1
  6. Polygon(B_2, A_2, n) → B, k, q_1, t_1, h_2, l_2, m_2, r_2, a_2, d_2, g_3, j_3, l, m_3, q_3, t_3, c_3, f_4, i_4, l_4, p_4, s_4, b_4, m, e_4, I, K, M, O, Q, T, W, B_1, E_1, s, H_1, L_1, M_1, Q_1, T_1, W_1, E_2, H_2, K_2, N_2, c_1, Q_2, T_2, W_2, B_3, E_3, H_3, K_3, N_3, Q_3, e_1, g_1, j_1, m_1
  7. Polygon(A_2, C_2, n) → A, p, r_1, f_2, i_2, n_2, p_2, s_2, b_2, e_2, h_3, k_3, q, n_3, r_3, a_3, d_3, g_4, j_4, m_4, q_4, t_4, c_4, r, f_5, J, L, N, P, R, U, Z, C_1, F_1, t, I_1, N_1, O_1, R_1, U_1, Z_1, F_2, I_2, L_2, O_2, d_1, R_2, U_2, Z_2, C_3, F_3, I_3, L_3, O_3, R_3, f_1, h_1, k_1, n_1
  8. Intersect(a_1, b_1) → S_3
  9. Point(a) → T_3
  10. Intersect(a, a_1) → U_3
  11. Polygon(S_3, T_3, U_3) → t1, u_3, g_5, h_5
  12. Angle(U_3, T_3, S_3) → α

AI Drawing Prompt Reference

Draw a right triangle with three polygons to illustrate the Pythagorean theorem. Start by drawing the two legs of the right triangle, then draw perpendicular lines from the right angle vertex to one leg, forming three polygons. Label the lengths of the sides and show the relationship between the hypotenuse and the sides of the smaller polygons to prove the Pythagorean theorem.
The prompt above was compiled from the original drawing commands and is for reference only.