Pythagoras without the squares demonstration
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This example dynamically demonstrates an obvious extension of the Pythagorean theorem without involving squares, focusing on right triangles, distance formulas, and vector operations. It utilizes GeoGebra commands like Segment, OrthogonalLine, Point, Polygon, and Angle for construction. Ideal for high school mathematics education to understand the geometric meaning and vector representation of the theorem.
GeoGebra Commands & Parameters
Segment(A, B) → aOrthogonalLine(B, a) → bPoint(b) → CSegment(C, B) → cSegment(C, A) → dPolygon(A, C, n) → poly1, e, n_1, b_{16}, D, E, J, M, P, S, V, A_1, D_1, r_1, G_1, J_1, M_1, P_1, S_1, V_1, A_2, D_2, G_2, J_2, a_2, M_2, P_2, S_2, V_2, A_3, D_3, G_3, J_3, M_3, P_3, d_2, S_3, V_3, A_4, D_4, G_4, J_4, M_4, P_4, S_4, V_4, g_2, A_5, D_5, G_5, J_5, M_5, P_5, S_5, V_5, A_6, D_6, j_2, G_6, J_6, M_6, P_6, S_6, V_6, A_7, D_7, G_7, J_7, m_2, M_7, P_7, S_7, V_7, A_8, D_8, G_8, J_8, M_8, P_8, q_2, S_8, V_8, A_9, D_9, G_9, J_9, M_9, P_9, S_9, V_9, t_2, A_{10}, D_{10}, G_{10}, J_{10}, M_{10}, P_{10}, S_{10}, V_{10}, A_{11}, D_{11}, c_3, G_{11}, J_{11}, M_{11}, P_{11}, S_{11}, V_{11}, A_{12}, D_{12}, G_{12}, f, f_3, i_3, l_3, p_3, s_3, e_4, h_4, k_4, n_4, r_4, g, a_5, d_5, g_5, j_5, m_5, q_5, t_5, c_6, f_6, i_6, h, l_6, p_6, s_6, b_7, e_7, h_7, k_7, n_7, r_7, a_8, s, d_8, g_8, j_8, m_8, q_8, t_8, c_9, f_9, i_9, l_9, b_1, p_9, s_9, b_{10}, e_{10}, h_{10}, k_{10}, n_{10}, r_{10}, a_{11}, d_{11}, e_1, g_{11}, j_{11}, m_{11}, q_{11}, t_{11}, c_{12}, f_{12}, i_{12}, l_{12}, p_{12}, h_1, s_{12}, b_{13}, e_{13}, h_{13}, k_{13}, n_{13}, r_{13}, a_{14}, d_{14}, g_{14}, k_1, j_{14}, m_{14}, q_{14}, t_{14}, c_{15}, f_{15}, i_{15}, l_{15}, p_{15}, s_{15}Polygon(C, B, n) → poly2, i, p_1, c_{16}, F, G, K, N, Q, T, W, B_1, E_1, s_1, H_1, K_1, N_1, Q_1, T_1, W_1, B_2, E_2, H_2, K_2, b_2, N_2, Q_2, T_2, W_2, B_3, E_3, H_3, K_3, N_3, Q_3, e_2, T_3, W_3, B_4, E_4, H_4, K_4, N_4, Q_4, T_4, W_4, h_2, B_5, E_5, H_5, K_5, N_5, Q_5, T_5, W_5, B_6, E_6, k_2, H_6, K_6, N_6, Q_6, T_6, W_6, B_7, E_7, H_7, K_7, n_2, N_7, Q_7, T_7, W_7, B_8, E_8, H_8, K_8, N_8, Q_8, r_2, T_8, W_8, B_9, E_9, H_9, K_9, N_9, Q_9, T_9, W_9, a_3, B_{10}, E_{10}, H_{10}, K_{10}, N_{10}, Q_{10}, T_{10}, W_{10}, B_{11}, E_{11}, d_3, H_{11}, K_{11}, N_{11}, Q_{11}, T_{11}, W_{11}, B_{12}, E_{12}, H_{12}, j, g_3, j_3, m_3, q_3, t_3, f_4, i_4, l_4, p_4, s_4, k, b_5, e_5, h_5, k_5, n_5, r_5, a_6, d_6, g_6, j_6, l, m_6, q_6, t_6, c_7, f_7, i_7, l_7, p_7, s_7, b_8, t, e_8, h_8, k_8, n_8, r_8, a_9, d_9, g_9, j_9, m_9, c_1, q_9, t_9, c_{10}, f_{10}, i_{10}, l_{10}, p_{10}, s_{10}, b_{11}, e_{11}, f_1, h_{11}, k_{11}, n_{11}, r_{11}, a_{12}, d_{12}, g_{12}, j_{12}, m_{12}, q_{12}, i_1, t_{12}, c_{13}, f_{13}, i_{13}, l_{13}, p_{13}, s_{13}, b_{14}, e_{14}, h_{14}, l_1, k_{14}, n_{14}, r_{14}, a_{15}, d_{15}, g_{15}, j_{15}, m_{15}, q_{15}, t_{15}Polygon(B, A, n) → poly3, m, q_1, d_{16}, H, I, L, O, R, U, Z, C_1, F_1, t_1, I_1, L_1, O_1, R_1, U_1, Z_1, C_2, F_2, I_2, L_2, c_2, O_2, R_2, U_2, Z_2, C_3, F_3, I_3, L_3, O_3, R_3, f_2, U_3, Z_3, C_4, F_4, I_4, L_4, O_4, R_4, U_4, Z_4, i_2, C_5, F_5, I_5, L_5, O_5, R_5, U_5, Z_5, C_6, F_6, l_2, I_6, L_6, O_6, R_6, U_6, Z_6, C_7, F_7, I_7, L_7, p_2, O_7, R_7, U_7, Z_7, C_8, F_8, I_8, L_8, O_8, R_8, s_2, U_8, Z_8, C_9, F_9, I_9, L_9, O_9, R_9, U_9, Z_9, b_3, C_{10}, F_{10}, I_{10}, L_{10}, O_{10}, R_{10}, U_{10}, Z_{10}, C_{11}, F_{11}, e_3, I_{11}, L_{11}, O_{11}, R_{11}, U_{11}, Z_{11}, C_{12}, F_{12}, I_{12}, p, h_3, k_3, n_3, r_3, d_4, g_4, j_4, m_4, q_4, t_4, q, c_5, f_5, i_5, l_5, p_5, s_5, b_6, e_6, h_6, k_6, r, n_6, r_6, a_7, d_7, g_7, j_7, m_7, q_7, t_7, c_8, a_1, f_8, i_8, l_8, p_8, s_8, b_9, e_9, h_9, k_9, n_9, d_1, r_9, a_{10}, d_{10}, g_{10}, j_{10}, m_{10}, q_{10}, t_{10}, c_{11}, f_{11}, g_1, i_{11}, l_{11}, p_{11}, s_{11}, b_{12}, e_{12}, h_{12}, k_{12}, n_{12}, r_{12}, j_1, a_{13}, d_{13}, g_{13}, j_{13}, m_{13}, q_{13}, t_{13}, c_{14}, f_{14}, i_{14}, m_1, l_{14}, p_{14}, s_{14}, b_{15}, e_{15}, h_{15}, k_{15}, n_{15}, r_{15}, a_{16}Angle(C, B, A) → αPolygon(A, B, C) → poly4, c_4, a_4, b_4
AI Drawing Prompt Reference
Draw a right triangle with labeled legs and hypotenuse. Extend the legs to form squares, connect their diagonals, and demonstrate the Pythagorean theorem geometrically. Represent the triangle and squares with vectors to show their relationships.
The prompt above was compiled from the original drawing commands and is for reference only.