Centre del quadrat
del catet més gran 

Paral·lela i perpendicular a la 
hipotenusa que passen pel centre

Punts mitjans dels costats
del quadrat de la hipotenusa

Paralel·lels als catets que
passen pels punts mitjans

Són congruents aquests
quatre quadrilàters?
Per què?

Triangle rectangle

Quadrats per a cada costat

Construeix, a l'interior de Q3, els quadrilàters
congruents amb R1, R2, R3, R4 i Q2 i digues
per què ho són.

Queda demostrat el teorema de Pitàgores?
Per què?

Etapa

Quatre parts iguals?

Segments

Auxiliars 1

Auxiliars 2

B = (-8.0752966909091, 3.6312649818181884)
C = (-2.5351422909091097, 3.534634381818188)
a_1 = Segment(B, C)
C_1 = Midpoint(a_1)
A' = Rotate(B, -90*°, C_1)
α = Angle(A', C_1, B)
c_2 = CircleArc(C_1, A', B)
A = Point(c_2)
Polígon1, c, a, b = Polygon(A, B, C)
Q3, e, f, g, h, D_4, E_3 = Polygon(C, B, 4)
Q1, i, j, k, l, F_4, G_4 = Polygon(A, C, 4)
Q2, m, n, p, q, H_3, I_3 = Polygon(B, A, 4)
r = Segment(G_4, C)
s = Segment(F_4, A)
J_4 = Intersect(r, s)
t = Line(J_4, a_1)
b_1 = OrthogonalLine(J_4, t)
K_4, L_4 = Intersect(t, Q1)
M_4, N_4 = Intersect(b_1, Q1)
O_3 = Intersect(b, i)
cc = Segment(G_4, K_4)
ee = Segment(G_4, N_4)
γ = Angle(G_4, N_4, J_4)
gg = Segment(N_4, J_4)
B_1 = (-5.64, 0.48)
C_2 = (-0.42, 0.36)
a_2 = Segment(B_1, C_2)
C_3 = Midpoint(a_2)
A'_1 = Rotate(B_1, -90*°, C_3)
α_1 = Angle(A'_1, C_3, B_1)
c_3 = CircleArc(C_3, A'_1, B_1)
A_1 = Point(c_3)
Polígon1_1, b_3, d_3, a_3 = Polygon(A_1, B_1, C_2)
Polígon3_1, i_1, j_1, k_1, l_1, F_1, G_1 = Polygon(A_1, C_2, 4)
r_3 = Segment(G_1, C_2)
s_3 = Segment(F_1, A_1)
J_1 = Intersect(r_3, s_3)
t_1 = Line(J_1, a_2)
b_2 = OrthogonalLine(J_1, t_1)
K_1, L_1 = Intersect(t_1, Polígon3_1)
M_1, N_1 = Intersect(b_2, Polígon3_1)
cc_1 = Segment(G_1, K_1)
o: abs(cc_1)
ee_1 = Segment(G_1, N_1)
γ_1 = Angle(G_1, N_1, J_1)
gg_1 = Segment(N_1, J_1)
B_2 = (-0.38, -0.06)
C_4 = (4.84, -0.18)
a_4 = Segment(B_2, C_4)
C_5 = Midpoint(a_4)
A'_2 = Rotate(B_2, -90*°, C_5)
α_2 = Angle(A'_2, C_5, B_2)
c_5 = CircleArc(C_5, A'_2, B_2)
A_2 = Point(c_5)
Polígon1_2, b_5, d_5, a_5 = Polygon(A_2, B_2, C_4)
Polígon3_2, i_2, j_2, k_2, l_2, F_2, G_2 = Polygon(A_2, C_4, 4)
r_5 = Segment(G_2, C_4)
s_5 = Segment(F_2, A_2)
J_2 = Intersect(r_5, s_5)
t_2 = Line(J_2, a_4)
b_4 = OrthogonalLine(J_2, t_2)
K_2, L_2 = Intersect(t_2, Polígon3_2)
M_2, N_2 = Intersect(b_4, Polígon3_2)
cc_2 = Segment(G_2, K_2)
u: abs(cc_2)
ee_2 = Segment(G_2, N_2)
γ_2 = Angle(G_2, N_2, J_2)
gg_2 = Segment(N_2, J_2)
B_3 = (2.86, -0.12)
C_6 = (8.08, -0.24)
a_6 = Segment(B_3, C_6)
C_7 = Midpoint(a_6)
A'_3 = Rotate(B_3, -90*°, C_7)
α_3 = Angle(A'_3, C_7, B_3)
c_7 = CircleArc(C_7, A'_3, B_3)
A_3 = Point(c_7)
Polígon1_3, b_7, d_7, a_7 = Polygon(A_3, B_3, C_6)
Polígon3_3, i_3, j_3, k_3, l_3, F_3, G_3 = Polygon(A_3, C_6, 4)
r_7 = Segment(G_3, C_6)
s_7 = Segment(F_3, A_3)
J_3 = Intersect(r_7, s_7)
t_3 = Line(J_3, a_6)
b_6 = OrthogonalLine(J_3, t_3)
K_3, L_3 = Intersect(t_3, Polígon3_3)
M_3, N_3 = Intersect(b_6, Polígon3_3)
cc_3 = Segment(G_3, K_3)
v: abs(cc_3)
ee_3 = Segment(G_3, N_3)
γ_3 = Angle(G_3, N_3, J_3)
gg_3 = Segment(N_3, J_3)
C_8 = (24.75, -0.528)
R1, n_1, g_2, k_4, j_4 = Polygon(N_4, G_4, K_4, J_4)
T = (9.189370509090912, 11.0718211818182)
U = Point(Circle[T, n_1])
V = Rotate(U + (g_2, 0), Angle[K_4 - G_4] + Angle[U - T] - Angle[G_4 - N_4], U)
W = Rotate(V + (k_4, 0), Angle[J_4 - K_4] + Angle[V - U] - Angle[K_4 - G_4], V)
Peça1, t_4, u_1, v_1, w = Polygon(T, U, V, W)
Z = (13.827639309090914, 11.812655781818199)
D_1 = Point(Circle[Z, n_1])
E_1 = Rotate(D_1 + (g_2, 0), Angle[K_4 - G_4] + Angle[D_1 - Z] - Angle[G_4 - N_4], D_1)
H_1 = Rotate(E_1 + (k_4, 0), Angle[J_4 - K_4] + Angle[E_1 - D_1] - Angle[K_4 - G_4], E_1)
Peça2, z, d_2, e_2, h_1 = Polygon(Z, D_1, E_1, H_1)
I_1 = (8.54516650909091, 6.304711581818195)
O_1 = Point(Circle[I_1, n_1])
P_1 = Rotate(O_1 + (g_2, 0), Angle[K_4 - G_4] + Angle[O_1 - I_1] - Angle[G_4 - N_4], O_1)
Q_1 = Rotate(P_1 + (k_4, 0), Angle[J_4 - K_4] + Angle[P_1 - O_1] - Angle[K_4 - G_4], P_1)
Peça3, i_4, o_1, p_2, q_2 = Polygon(I_1, O_1, P_1, Q_1)
R_1 = (12.925753709090912, 6.562393181818195)
S_1 = Point(Circle[R_1, n_1])
T_1 = Rotate(S_1 + (g_2, 0), Angle[K_4 - G_4] + Angle[S_1 - R_1] - Angle[G_4 - N_4], S_1)
U_1 = Rotate(T_1 + (k_4, 0), Angle[J_4 - K_4] + Angle[T_1 - S_1] - Angle[K_4 - G_4], T_1)
Peça4, r_2, s_2, t_5, u_2 = Polygon(R_1, S_1, T_1, U_1)
Quadrat, a_8, h_2, i_5, b_8 = Polygon(A, H_3, I_3, B)
P_3 = (10.671039709090913, 1.763073381818191)
Q = Point(Circle[P_3, a_8])
R = Rotate(Q + (h_2, 0), Angle[I_3 - H_3] + Angle[Q - P_3] - Angle[H_3 - A], Q)
S = Rotate(R + (i_5, 0), Angle[B - I_3] + Angle[R - Q] - Angle[I_3 - H_3], R)
Peça5, p_1, q_1, r_1, s_1 = Polygon(P_3, Q, R, S)
c_1 = Segment(N_4, J_4)
d_1 = Segment(J_4, L_4)
e_1 = Segment(K_4, J_4)
f_1 = Segment(J_4, M_4)
V_1 = Intersect(a, e)
W_1 = Midpoint(a)
Z_1 = Midpoint(h)
D_2 = Midpoint(f)
E_2 = Midpoint(g)
d = Line(W_1, c)
g_1 = Line(D_2, b)
m_1 = Line(Z_1, b)
f_2 = Line(E_2, c)
H_2 = Intersect(m_1, f_2)
I_2 = Intersect(d, m_1)
O_2 = Intersect(d, g_1)
P_2 = Intersect(g_1, f_2)
Q_2, R_2 = Intersect(m_1, Q3)
S_2, T_2 = Intersect(d, Q3)
U_2, V_2 = Intersect(g_1, Q3)
W_2, Z_2 = Intersect(f_2, Q3)
m_2 = Segment(R_2, Z_1)
n_2 = Segment(D_2, U_2)
e_3 = Segment(W_1, T_2)
f_3 = Segment(W_2, E_2)
Etapa = 1 (slider from 1 to 8, step 1)
β, δ, ε = Angle(Polígon1)
R2, f_4, n_3, j_5, l_4 = Polygon(F_4, N_4, J_4, L_4)
D_3 = Point(d_1)
R3, j_6, m_3, c_4, d_4 = Polygon(J_4, M_4, C, D_3)
R4, j_7, k_5, a_9, m_4 = Polygon(J_4, K_4, A, M_4)
Polígon2, a_{10}, h_3, i_6, b_9 = Polygon(A, H_3, I_3, B)
D = (-1.2, -0.76)
E = (2.68, -0.76)
Polígon3, g_3, p_3, q_3, e_4, F, G = Polygon(D, E, 4)
g_4 = Segment(G, E)
h_4 = Segment(F, D)
H = Intersect(g_4, h_4)
I = Point(q_3)
n_4 = Ray(I, H)
J = Intersect(n_4, g_3)
p_4 = Segment(I, H)
q_4 = Segment(H, J)
r_4 = OrthogonalLine(H, p_4)
K, L = Intersect(r_4, Polígon3)
s_4 = Segment(K, H)
e_5 = Segment(H, L)
f_5 = Segment(I, H)
g_5 = Segment(L, H)
h_5 = Segment(H, J)
l_5 = Segment(H, K)
w_1 = false
m_5 = OrthogonalLine(H, q_3)
n_5 = OrthogonalLine(H, m_5)
o_2 = false
M, N = Intersect(m_5, Polígon3)
O, P = Intersect(n_5, Polígon3)
Polígon4, p_5, u_3, q_5 = Polygon(M, I, H)
Polígon5, z_3, t_6, p_6 = Polygon(L, H, P)
Polígon6, v_3, r_6, p_7 = Polygon(J, H, N)
Polígon7, w_3, s_6, p_8 = Polygon(K, H, O)
v_2 = false
text9: "  " + (Etapa - 1) + "  "