Pitágoras
Author: José María Vázquez de la Torre Prieto

En el triángulo ABC, sobre los lados que forman el ángulo recto hemos construido cuadrados.
a) Construye tú el cuadrado que corresponde a la hipotenusa. (lado opuesto al ángulo recto).
b) Construye  los tres cuadrados correspondientes en el triángulo DEF.
c) ¿Observas alguna relación entre las áreas de los cuadrados de cada triángulo?
d) ¿Ocurre lo mismo en el triángulo GHI? ¿Por qué?

Utiliza las herramientas del menú superior para dibujar los cuadrados y calcular sus áreas.

Comprueba la solución, marcando en cada una de las casillas de control de cada pregunta.

Construcción realizada por José María Vázquez de la Torre Prieto

http://www.matesymas.es/
@matesymas

En el triángulo ABC hemos dibujado 2 cuadrados sobre los lados que forman el ángulo recto

A

B

C

Dibuja el cuadrado que corresponde a la hipotenusa del triángulo ABC.

a)

Dibuja los 3 cuadrados correspondientes a los lados del triángulo DEF.

b)

¿Observas alguna relación entre las áreas de los cuadrados de cada triángulo?

c)

¿Ocurre lo mismo en el triángulo GHI? ¿Por qué?

d)

A_{14} = (-3, 5)
B_{14} = (-3, 4)
C_{14} = (-3, 3)
D_{14} = (-3, 2)
C = (-2, 1)
F_{14} = Point(xAxis)
G_5 = (-3, -1)
H_{14} = (-3, -2)
I_{14} = (-3, -3)
J = (-3, -4)
K = (-3, -5)
L = (-3, -6)
M = (-2, 5)
N = (-2, 4)
O = (-2, 3)
P = (-2, 2)
Q = (-3, 1)
R = (-2, 0)
S = (-2, -1)
T = (-2, -2)
U = (-2, -3)
V = (-2, -4)
W = (-2, -5)
Z = (-2, -6)
A_1 = (-1, 5)
B_1 = (-1, 4)
C_1 = (-1, 3)
D_1 = (-1, 2)
E_1 = (-1, 1)
F_1 = Point(xAxis)
G_1 = (-1, -1)
H_1 = (-1, -2)
I_1 = (-1, -3)
J_1 = (-1, -4)
K_1 = (-1, -5)
L_1 = (-1, -6)
A = Point(yAxis)
N_1 = Point(yAxis)
O_1 = (0, 3)
P_1 = (0, 2)
B = (0, 1)
R_1 = (0, 0)
S_1 = (0, -1)
T_1 = (0, -2)
U_1 = (0, -3)
V_1 = (0, -4)
W_1 = (0, -5)
Z_1 = (0, -6)
A_2 = (1, 5)
B_2 = (1, 4)
C_2 = (1, 3)
D_2 = (1, 2)
E_2 = (1, 1)
F_2 = (1, 0)
G_2 = (1, -1)
H_2 = (1, -2)
I_2 = (1, -3)
J_2 = (1, -4)
K_2 = (1, -5)
L_2 = (1, -6)
M_2 = (2, 5)
N_2 = (2, 4)
O_2 = (2, 3)
P_2 = (2, 2)
Q_2 = (2, 1)
R_2 = (2, 0)
S_2 = (2, -1)
T_2 = (2, -2)
U_2 = (2, -3)
V_2 = (2, -4)
W_2 = (2, -5)
Z_2 = (2, -6)
A_3 = (3, 5)
B_3 = (3, 4)
C_3 = (3, 3)
D_3 = (3, 2)
E_3 = (3, 1)
F_3 = (3, 0)
G_3 = (3, -1)
H_3 = (3, -2)
I_3 = (3, -3)
J_3 = (3, -4)
K_3 = (3, -5)
L_3 = (3, -6)
M_3 = (4, 5)
N_3 = (4, 4)
O_3 = (4, 3)
P_3 = (4, 2)
Q_3 = (4, 1)
R_3 = (5, 0)
S_3 = (4, 0)
T_3 = (4, -1)
U_3 = (4, -2)
V_3 = (4, -3)
W_3 = (4, -4)
Z_3 = (4, -5)
A_4 = (4, -6)
B_4 = (5, 5)
C_4 = (6, 5)
D_4 = (7, 5)
E_4 = (8, 5)
F_4 = (9, 5)
G_4 = (5, 4)
H_4 = (6, 4)
I_4 = (7, 4)
J_4 = (8, 4)
K_4 = (9, 4)
L_4 = (5, 3)
M_4 = (6, 3)
N_4 = (7, 3)
O_4 = (8, 3)
P_4 = (9, 3)
Q_4 = (5, 2)
R_4 = (6, 2)
S_4 = (7, 2)
T_4 = (8, 2)
U_4 = (9, 2)
V_4 = (5, 1)
W_4 = (6, 1)
Z_4 = (7, 1)
A_5 = (8, 1)
B_5 = (9, 1)
C_5 = (6, 0)
D_5 = (7, 0)
E_5 = (8, 0)
F_5 = (9, 0)
F = (7, -2)
H_5 = (6, -1)
I_5 = (7, -1)
J_5 = (8, -1)
K_5 = (9, -1)
L_5 = (6, -2)
M_5 = (5, -2)
N_5 = (7, -2)
O_5 = (8, -2)
P_5 = (9, -2)
Q_5 = (5, -3)
R_5 = (6, -3)
S_5 = (7, -3)
T_5 = (8, -3)
U_5 = (9, -3)
V_5 = (5, -4)
W_5 = (6, -4)
Z_5 = (7, -4)
E = (9, -4)
B_6 = (9, -4)
C_6 = (5, -5)
D_6 = (6, -5)
E_6 = (7, -5)
F_6 = (8, -5)
G_6 = (9, -5)
H_6 = (5, -6)
I_6 = (6, -6)
J_6 = (7, -6)
K_6 = (8, -6)
L_6 = (9, -6)
M_6 = (10, 5)
N_6 = (11, 5)
O_6 = (12, 5)
P_6 = (13, 5)
Q_6 = (14, 5)
R_6 = (15, 5)
S_6 = (16, 5)
T_6 = (17, 5)
U_6 = (18, 5)
V_6 = (19, 5)
W_6 = (20, 5)
Z_6 = (21, 5)
A_7 = (10, 4)
B_7 = (11, 4)
C_7 = (12, 4)
D_7 = (13, 4)
E_7 = (14, 4)
F_7 = (15, 4)
G_7 = (16, 4)
H_7 = (17, 4)
I_7 = (18, 4)
J_7 = (19, 4)
K_7 = (20, 4)
L_7 = (21, 4)
M_7 = (10, 3)
N_7 = (11, 3)
O_7 = (12, 3)
P_7 = (13, 3)
Q_7 = (14, 3)
R_7 = (15, 3)
S_7 = (16, 3)
T_7 = (17, 3)
U_7 = (18, 3)
V_7 = (19, 3)
W_7 = (20, 3)
Z_7 = (21, 3)
A_8 = (10, 2)
B_8 = (11, 2)
C_8 = (12, 2)
D_8 = (13, 2)
E_8 = (15, 1)
F_8 = (15, 2)
G_8 = (16, 2)
H_8 = (17, 2)
I_8 = (18, 2)
J_8 = (19, 2)
K_8 = (20, 2)
L_8 = (21, 2)
M_8 = (10, 1)
N_8 = (11, 1)
O_8 = (12, 1)
P_8 = (13, 1)
Q_8 = (14, 1)
G = (15, 1)
S_8 = (16, 1)
T_8 = (17, 1)
U_8 = (18, 1)
V_8 = (19, 1)
W_8 = (20, 1)
Z_8 = (21, 1)
A_9 = (10, 0)
B_9 = (11, 0)
C_9 = (12, 0)
D_9 = (13, 0)
E_9 = (14, 0)
F_9 = (15, 0)
G_9 = (16, 0)
H_9 = (17, 0)
I_9 = (18, 0)
I = (18, -1)
K_9 = (20, 0)
L_9 = (21, 0)
M_9 = (10, -1)
D = (11, -2)
O_9 = (12, -1)
P_9 = (13, -1)
Q_9 = (14, -1)
R_9 = (15, -1)
S_9 = (16, -1)
T_9 = (17, -1)
U_9 = (18, -1)
V_9 = (19, -1)
W_9 = (20, -1)
Z_9 = (21, -1)
A_{10} = (10, -2)
B_{10} = (11, -2)
C_{10} = (12, -2)
D_{10} = (13, -2)
E_{10} = (14, -2)
F_{10} = (15, -2)
G_{10} = (16, -2)
H_{10} = (17, -2)
I_{10} = (18, -2)
J_{10} = (19, -1)
K_{10} = (20, -2)
L_{10} = (21, -2)
M_{10} = (10, -3)
N_{10} = (11, -3)
O_{10} = (12, -3)
P_{10} = (13, -3)
Q_{10} = (14, -3)
R_{10} = (15, -3)
S_{10} = (16, -3)
H = (16, -2)
U_{10} = (18, -3)
V_{10} = (19, -3)
W_{10} = (20, -3)
Z_{10} = (21, -3)
A_{11} = (10, -4)
B_{11} = (11, -4)
C_{11} = (12, -4)
D_{11} = (13, -4)
E_{11} = (14, -4)
F_{11} = (15, -4)
G_{11} = (16, -4)
H_{11} = (17, -4)
I_{11} = (18, -4)
J_{11} = (19, -4)
K_{11} = (20, -4)
L_{11} = (21, -4)
M_{11} = (10, -5)
N_{11} = (11, -5)
O_{11} = (12, -5)
P_{11} = (13, -5)
Q_{11} = (14, -5)
R_{11} = (15, -5)
S_{11} = (16, -5)
T_{11} = (17, -5)
U_{11} = (18, -5)
V_{11} = (19, -5)
W_{11} = (20, -5)
Z_{11} = (21, -5)
A_{12} = (10, -6)
B_{12} = (11, -6)
C_{12} = (12, -6)
D_{12} = (13, -6)
E_{12} = (14, -6)
F_{12} = (15, -6)
G_{12} = (16, -6)
H_{12} = (17, -6)
I_{12} = (18, -6)
J_{12} = (19, -6)
K_{12} = (20, -6)
L_{12} = (21, -6)
polígono1, e, m_1, q_1 = Polygon(A, B, C)
polígono2, m_2, q_2, a, b, M_{12}, N_{12} = Polygon(A, B, 4)
polígono3, q_3, e_1, c, d, O_{12}, P_{12} = Polygon(B, C, 4)
Q_{12} = (5, -1)
polígono4, a_6, g_5, n_9 = Polygon(F, D, E)
polígono5, a_1, g_1, f, g, R_{12}, S_{12} = Polygon(E, F, 4)
polígono6, n_1, a_2, h, i, T_{12}, U_{12} = Polygon(D, E, 4)
polígono7, g_2, n_2, j, k, V_{12}, W_{12} = Polygon(F, D, 4)
polígono8, j_9, e_8, t_{10} = Polygon(E_8, H, I)
polígono9, t_1, e_2, l, m, Z_{12}, A_{13} = Polygon(H, E_8, 4)
polígono10, j_1, t_2, n, p, B_{13}, C_{13} = Polygon(I, H, 4)
polígono11, e_3, j_2, q, r, D_{13}, E_{13} = Polygon(E_8, I, 4)
α = Angle(G, H, J_{10})
F_{13} = Point(a_2)
G_{13} = (14, 2)
H_{13} = (19, 0)
I_{13} = (22, 5)
J_{13} = (22, 4)
K_{13} = (22, 3)
L_{13} = Intersect(q, j_2)
M_{13} = (22, 1)
N_{13} = (22, 0)
O_{13} = (22, -1)
P_{13} = (22, -2)
Q_{13} = (22, -3)
R_{13} = (22, -4)
S_{13} = (22, -5)
T_{13} = (22, -6)
M_1 = (0, -1)
Q_1 = (0, -5)
A_6 = (-2, -5)
polígono12, a_3, m_3, q_4 = Polygon(M_1, Q_1, A_6)
polígono13, o_1, e_4, b_1 = Polygon(E_1, B, O_1)
R_8 = Intersect(e_4, o_1)
polígono14, r_8, e_5, s, t, J_9, N_9 = Polygon(R_8, E_1, 4)
T_{10} = Intersect(b_1, e_4)
polígono15, t_3, r_1, c_1, d_1, U_{13}, V_{13} = Polygon(T_{10}, R_8, 4)
W_{13} = Intersect(b_1, o_1)
polígono16, w_{13}, t_4, f_1, h_1, Z_{13}, E_{14} = Polygon(W_{13}, T_{10}, 4)
o = false
u = false
Textopolígono16: "Area = " + polígono16
Textopolígono15: "Area = " + polígono15
Textopolígono14: "Area = " + polígono14
Textopolígono7: "Area = " + polígono7
Textopolígono5: "Area = " + polígono5
Textopolígono6: "Area = " + polígono6
v = false
Textopolígono9: "Area = " + polígono9
Textopolígono10: "Area = " + polígono10
Textopolígono11: "Area = " + polígono11
G_{14} = (11, -1)
w = false