Delta, oef.1 p.118

Bepaal eerst zelf of de figuren congruent zijn.
Gebruik dan de schuifbalk om je antwoord te controleren.

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

A = (-6, 8.4)
B = (-4.8, 8.4)
C = (-3.5999999999999996, 6.6)
D = (-6, 6.6)
P, a_5, b_5, c, d = Polygon(A, B, C, D)
E = (-2.4, 7.8)
F = (-1.2, 7.8)
G = (0, 6)
H = (-2.4, 6)
Q, e, f, g, h = Polygon(E, F, G, H)
i = 0 (slider from 0 to 1, step 0.01)
u = Vector(B, B + i * (F - B))
A' = Translate(A, u)
B' = Translate(B, u)
C' = Translate(C, u)
D' = Translate(D, u)
P', a', b', c', d' = Polygon(A', B', C', D')
I = (1.7999999999999998, 8.4)
J = (3.5999999999999996, 8.4)
K = (2.7, 6)
R, k, i_1, j = Polygon(I, J, K)
L = (5.3999999999999995, 7.8)
M = (6.6, 5.3999999999999995)
N = (4.2, 5.3999999999999995)
S, n, l, m = Polygon(L, M, N)
o = 0 (slider from 0 to 1, step 0.01)
p = LineBisector(k)
q = LineBisector(j)
O = Intersect(q, p)
ro1: sqrt(0.5 - o) 0
I' = Rotate(I, -(ro1 + 360 o) °, O)
J' = Rotate(J, -(ro1 + 360 o) °, O)
K' = Rotate(K, -(ro1 + 360 o) °, O)
R', k', i', j' = Polygon(I', J', K')
I'_1 = Rotate(I, 180°, O)
J'_1 = Rotate(J, 180°, O)
K'_1 = Rotate(K, 180°, O)
R'_1, k'_1, i'_1, j'_1 = Polygon(I'_1, J'_1, K'_1)
tr1: sqrt(o - 0.5) 0
v = Vector(J'_1, J'_1 + (tr1 + 2 o - 1) * (N - J'_1))
I'_1' = Translate(I'_1, v)
J'_1' = Translate(J'_1, v)
K'_1' = Translate(K'_1, v)
R'_1', k'_1', i'_1', j'_1' = Polygon(I'_1', J'_1', K'_1')
T = (7.8, 7.199999999999999)
U = (8.4, 8.4)
V = (11.4, 8.4)
W = (10.799999999999999, 7.199999999999999)
Y, t, u_1, v_1, w = Polygon(T, U, V, W)
Z = (8.4, 6.6)
A_1 = (11.4, 6.6)
B_1 = (12, 5.3999999999999995)
C_1 = (9, 5.3999999999999995)
P_1, z, a_1, b_1, c_1 = Polygon(Z, A_1, B_1, C_1)
r = 0 (slider from 0 to 1, step 0.01)
ro2: sqrt(0.5 - r) 0
F_1 = (8.4, 6)
bo1: sqrt(r - 0.49) 0 + 1
D_1 = (8.4, 6)
E_1 = (11.4, 6)
G_1 = Dilate(D_1, bo1, T)
H_1 = Dilate(E_1, bo1, W)
Q_1, t_1, w_1, h_1, g_1 = Polygon(T, W, H_1, G_1)
tr2: sqrt(r - 0.5) 0
s = Vector(G_1, G_1 + (tr2 + 2 r - 1) * (C_1 - G_1))
T' = Translate(T, s)
W' = Translate(W, s)
H_1' = Translate(H_1, s)
G_1' = Translate(G_1, s)
Q_1', t', w', h_1', g_1' = Polygon(T', W', H_1', G_1')
I_1 = (-5.3999999999999995, 2.4)
J_1 = (-5.3999999999999995, 3.5999999999999996)
d_1 = Circle(I_1, J_1)
K_1 = (-3.5999999999999996, 1.7999999999999998)
L_1 = (-3.5999999999999996, 3)
e_1 = Circle(K_1, L_1)
f_1 = 0 (slider from 0 to 1, step 0.01)
z_1 = Vector(I_1, I_1 + f_1 * (K_1 - I_1))
k_1 = Translate(d_1, z_1)
M_1 = (0, 3.5999999999999996)
N_1 = (-0.6, 2.4)
O_1 = (0, 1.2)
R_1 = (0.6, 2.4)
S_1, m_1, n_1, o_1, r_1 = Polygon(M_1, N_1, O_1, R_1)
T_1 = (1.2, 1.2)
U_1 = (1.7999999999999998, 2.4)
V_1 = (3, 2.4)
W_1 = (2.4, 1.2)
Y_1, t_2, u_2, v_2, w_2 = Polygon(T_1, U_1, V_1, W_1)
j_1 = 0 (slider from 0 to 1, step 0.01)
l_1 = Vector(N_1, U_1)
M_1' = Translate(M_1, l_1)
N_1' = Translate(N_1, l_1)
O_1' = Translate(O_1, l_1)
R_1' = Translate(R_1, l_1)
S_1', m_1', n_1', o_1', r_1' = Polygon(M_1', N_1', O_1', R_1')
α = Angle(T_1, N_1', O_1')
tr3: sqrt(0.5 - j_1) 0
p_1 = Vector(N_1, N_1 + (tr3 + 2 j_1) * (U_1 - N_1))
M_2 = Translate(M_1, p_1)
N_2 = Translate(N_1, p_1)
O_2 = Translate(O_1, p_1)
R_2 = Translate(R_1, p_1)
S_2, m_2, n_2, o_2, r_2 = Polygon(M_2, N_2, O_2, R_2)
ro3: sqrt(j_1 - 0.5) 0
M_1'' = Rotate(M_1', -(ro3 + 2 α j_1 - α), U_1)
N_1'' = Rotate(N_1', -(ro3 + 2 α j_1 - α), U_1)
O_1'' = Rotate(O_1', -(ro3 + 2 α j_1 - α), U_1)
R_1'' = Rotate(R_1', -(ro3 + 2 α j_1 - α), U_1)
S_1'', m_1'', n_1'', o_1'', r_1'' = Polygon(M_1'', N_1'', O_1'', R_1'')
Z_1 = (6.6, 3)
A_2 = (6.6, 2.4)
B_2 = (5.3999999999999995, 2.4)
C_2 = (5.3999999999999995, 1.7999999999999998)
D_2 = (6, 1.7999999999999998)
E_2 = (6, 1.2)
F_2 = (5.3999999999999995, 1.2)
G_2 = (5.3999999999999995, 0.6)
H_2 = (6.6, 0.6)
I_2 = (6.6, 0)
J_2 = (4.8, 0)
K_2 = (4.8, 3)
P_2, z_2, a_2, b_2, c_2, d_2, e_2, f_2, g_2, h_2, i_2, j_2, k_2 = Polygon(Z_1, A_2, B_2, C_2, D_2, E_2, F_2, G_2, H_2, I_2, J_2, K_2)
L_2 = (8.4, 1.2)
Q_2 = (9, 1.2)
T_2 = (9, 1.7999999999999998)
U_2 = (9.6, 1.7999999999999998)
V_2 = (9.6, 1.2)
W_2 = (10.2, 1.2)
Y_2 = (10.2, 3)
Z_2 = (10.799999999999999, 3)
A_3 = (10.799999999999999, 0.6)
B_3 = (7.8, 0.6)
C_3 = (7.8, 3)
D_3 = (8.4, 3)
P_3, l_2, q_2, t_3, u_3, v_3, w_3, y_2, z_3, a_3, b_3, c_3, d_3 = Polygon(L_2, Q_2, T_2, U_2, V_2, W_2, Y_2, Z_2, A_3, B_3, C_3, D_3)
q_1 = 0 (slider from 0 to 1, step 0.01)
tr4: sqrt(0.5 - q_1) 0
s_1 = Vector(J_2, J_2 + (tr4 + 2 q_1) * (A_3 - J_2))
Z_1' = Translate(Z_1, s_1)
A_2' = Translate(A_2, s_1)
B_2' = Translate(B_2, s_1)
C_2' = Translate(C_2, s_1)
D_2' = Translate(D_2, s_1)
E_2' = Translate(E_2, s_1)
F_2' = Translate(F_2, s_1)
G_2' = Translate(G_2, s_1)
H_2' = Translate(H_2, s_1)
I_2' = Translate(I_2, s_1)
J_2' = Translate(J_2, s_1)
K_2' = Translate(K_2, s_1)
P_2', z_1', a_2', b_2', c_2', d_2', e_2', f_2', g_2', h_2', i_2', j_2', k_2' = Polygon(Z_1', A_2', B_2', C_2', D_2', E_2', F_2', G_2', H_2', I_2', J_2', K_2')
p_2 = Vector(J_2, A_3)
Z_3 = Translate(Z_1, p_2)
A_4 = Translate(A_2, p_2)
B_4 = Translate(B_2, p_2)
C_4 = Translate(C_2, p_2)
D_4 = Translate(D_2, p_2)
E_3 = Translate(E_2, p_2)
F_3 = Translate(F_2, p_2)
G_3 = Translate(G_2, p_2)
H_3 = Translate(H_2, p_2)
I_3 = Translate(I_2, p_2)
J_3 = Translate(J_2, p_2)
K_3 = Translate(K_2, p_2)
P_4, z_4, a_4, b_4, c_4, d_4, e_3, f_3, g_3, h_3, i_3, j_3, k_3 = Polygon(Z_3, A_4, B_4, C_4, D_4, E_3, F_3, G_3, H_3, I_3, J_3, K_3)
ro4: sqrt(q_1 - 0.5) 0
Z_3' = Rotate(Z_3, (ro4 + 180 q_1 - 90) °, A_3)
A_4' = Rotate(A_4, (ro4 + 180 q_1 - 90) °, A_3)
B_4' = Rotate(B_4, (ro4 + 180 q_1 - 90) °, A_3)
C_4' = Rotate(C_4, (ro4 + 180 q_1 - 90) °, A_3)
D_4' = Rotate(D_4, (ro4 + 180 q_1 - 90) °, A_3)
E_3' = Rotate(E_3, (ro4 + 180 q_1 - 90) °, A_3)
F_3' = Rotate(F_3, (ro4 + 180 q_1 - 90) °, A_3)
G_3' = Rotate(G_3, (ro4 + 180 q_1 - 90) °, A_3)
H_3' = Rotate(H_3, (ro4 + 180 q_1 - 90) °, A_3)
I_3' = Rotate(I_3, (ro4 + 180 q_1 - 90) °, A_3)
J_3' = Rotate(J_3, (ro4 + 180 q_1 - 90) °, A_3)
K_3' = Rotate(K_3, (ro4 + 180 q_1 - 90) °, A_3)
P_4', z_3', a_4', b_4', c_4', d_4', e_3', f_3', g_3', h_3', i_3', j_3', k_3' = Polygon(Z_3', A_4', B_4', C_4', D_4', E_3', F_3', G_3', H_3', I_3', J_3', K_3')
L_3 = (-6.6, -1.7999999999999998)
M_3 = (-5.3999999999999995, -1.2)
N_3 = (-4.2, -1.7999999999999998)
O_3 = (-5.3999999999999995, -3.5999999999999996)
Q_3, l_3, m_3, n_3, o_3 = Polygon(L_3, M_3, N_3, O_3)
R_3 = (-3.5999999999999996, -2.4)
S_3 = (-3, -1.2)
T_3 = (-1.2, -2.4)
U_3 = (-3, -3.5999999999999996)
V_3, r_3, s_3, t_4, u_4 = Polygon(R_3, S_3, T_3, U_3)
s_2 = 0 (slider from 0 to 1, step 0.01)
tr5: sqrt(0.5 - s_2) 0
p_3 = Vector(M_3, M_3 + (tr5 + 2 s_2) * (R_3 - M_3))
L_3' = Translate(L_3, p_3)
M_3' = Translate(M_3, p_3)
N_3' = Translate(N_3, p_3)
O_3' = Translate(O_3, p_3)
Q_3', l_3', m_3', n_3', o_3' = Polygon(L_3', M_3', N_3', O_3')
q_3 = Vector(M_3, R_3)
L_4 = Translate(L_3, q_3)
M_4 = Translate(M_3, q_3)
N_4 = Translate(N_3, q_3)
O_4 = Translate(O_3, q_3)
Q_4, l_4, m_4, n_4, o_4 = Polygon(L_4, M_4, N_4, O_4)
ro5: sqrt(s_2 - 0.5) 0
M_4' = Rotate(M_4, (ro2 + 180 s_2 - 90) °, R_3)
O_4' = Rotate(O_4, (ro2 + 180 s_2 - 90) °, R_3)
L_4' = Rotate(L_4, (ro5 + 180 s_2 - 90) °, R_3)
M_5 = Rotate(M_4, (ro5 + 180 s_2 - 90) °, R_3)
N_4' = Rotate(N_4, (ro5 + 180 s_2 - 90) °, R_3)
O_5 = Rotate(O_4, (ro5 + 180 s_2 - 90) °, R_3)
Q_4', l_4', m_5, n_4', o_5 = Polygon(L_4', M_5, N_4', O_5)
A1 = (-7.066666666666666, 10.5)
B1 = (13.2, 10.466666666666667)
C1 = (13.2, 9)
D1 = (-7.066666666666666, 8.966666666666667)
E1 = (27.03333333333333, 10.433333333333334)
F1 = (27.233333333333334, -10.533333333333333)
G1 = (13.266666666666666, -10.4)
H1 = (-7.066666666666666, -5.4)
J1 = (-7.1, -10.366666666666667)
K1 = (0, -1.2)
L1 = (0, -3.5999999999999996)
M1 = (1.7999999999999998, -3.5999999999999996)
poly4, m1, k1, l1 = Polygon(K1, L1, M1)
N1 = (2.4, -3.5999999999999996)
O1 = (2.4, -1.2)
P1 = (4.8, -1.2)
poly5, p1, n1, o1 = Polygon(N1, O1, P1)
q1 = 0 (slider from 0 to 1, step 0.01)
bo2: sqrt(q1 - 0.15) 0 + 1
I1 = (0, -6)
Q1: bo2 I1
R1: bo2 L1
S1: bo2 M1
poly1, q1_1, r1, s1 = Polygon(R1, S1, Q1)
poly2, q1_2, r1_1, s1_1 = Polygon(R1, S1, Q1)
tr6: sqrt(q1 - 0.5) 0
poly3, q1_3, r1_2, s1_2 = Polygon(R1, S1, Q1)
u1 = Vector(Q1, Q1 + (tr6 + 2 q1 - 1) * (N1 - Q1))
R1' = Translate(R1, u1)
S1' = Translate(S1, u1)
Q1' = Translate(Q1, u1)
poly3', q1', r1', s1' = Polygon(R1', S1', Q1')
U1 = (6.6, -3.5999999999999996)
V1 = (7.8, -1.7999999999999998)
W1 = (5.3999999999999995, -1.7999999999999998)
c1 = CircleSector(U1, V1, W1)
Z1 = (10.799999999999999, -2.4)
A2 = (9, -1.2)
B2 = (9, -3.5999999999999996)
d1 = CircleSector(Z1, A2, B2)
a1 = 0 (slider from 0 to 1, step 0.01)
tr7: sqrt(0.5 - a1) 0
v1 = Vector(U1, U1 + (tr7 + 2 a1) * (Z1 - U1))
U1' = Translate(U1, v1)
V1' = Translate(V1, v1)
W1' = Translate(W1, v1)
e1 = Sector(Translate[Circle[U1, V1], v1], V1', W1')
w1 = Vector(U1, Z1)
U1'_1 = Translate(U1, w1)
V1'_1 = Translate(V1, w1)
W1'_1 = Translate(W1, w1)
f1 = Sector(Translate[Circle[U1, V1], w1], V1'_1, W1'_1)
ro6: sqrt(a1 - 0.5) 0
V1'_1' = Rotate(V1'_1, (ro1 + 180 a1 - 90) °, Z1)
W1'_1' = Rotate(W1'_1, (ro1 + 180 a1 - 90) °, Z1)
V1'_2 = Rotate(V1'_1, (ro6 + 180 a1 - 90) °, Z1)
W1'_2 = Rotate(W1'_1, (ro6 + 180 a1 - 90) °, Z1)
h1 = Sector(Rotate[Translate[Circle[U1, V1], w1], (ro6 + 180 a1 - 90) °, Z1], V1'_2, W1'_2)
C2 = (12, -0.6)
D2 = (13.799999999999999, -0.6)
E2 = (13.799999999999999, -1.7999999999999998)
F2 = (13.2, -1.7999999999999998)
G2 = (13.2, -1.2)
H2 = (12.6, -1.2)
I2 = (12.6, -3)
J2 = (13.2, -3)
K2 = (13.2, -2.4)
L2 = (13.799999999999999, -2.4)
M2 = (13.799999999999999, -3.5999999999999996)
N2 = (12, -3.5999999999999996)
poly6, c2, d2, e2, f2, g2, h2, i2, j2, k2, l2, m2, n2 = Polygon(C2, D2, E2, F2, G2, H2, I2, J2, K2, L2, M2, N2)
O2 = (16.8, -0.6)
P2 = (16.8, -3.5999999999999996)
Q2 = (15, -3.5999999999999996)
R2 = (15, -2.4)
S2 = (15.6, -2.4)
U2 = (15.6, -3)
V2 = (16.2, -3)
W2 = (16.2, -1.2)
Z2 = (15.6, -1.2)
A3 = (15.6, -1.7999999999999998)
B3 = (15, -1.7999999999999998)
C3 = (15, -0.6)
poly7, o2, p2, q2, r2, s2, u2, v2, w2, z2, a3, b3, c3 = Polygon(O2, P2, Q2, R2, S2, U2, V2, W2, Z2, A3, B3, C3)
b1 = 0 (slider from 0 to 1, step 0.01)
i1 = Segment(C2, M2)
j1 = Segment(N2, D2)
D3 = Intersect(i1, j1)
ro7: sqrt(0.5 - b1) 0
C2' = Rotate(C2, -(ro7 + 360 b1) °, D3)
D2' = Rotate(D2, -(ro7 + 360 b1) °, D3)
E2' = Rotate(E2, -(ro7 + 360 b1) °, D3)
F2' = Rotate(F2, -(ro7 + 360 b1) °, D3)
G2' = Rotate(G2, -(ro7 + 360 b1) °, D3)
H2' = Rotate(H2, -(ro7 + 360 b1) °, D3)
I2' = Rotate(I2, -(ro7 + 360 b1) °, D3)
J2' = Rotate(J2, -(ro7 + 360 b1) °, D3)
K2' = Rotate(K2, -(ro7 + 360 b1) °, D3)
L2' = Rotate(L2, -(ro7 + 360 b1) °, D3)
M2' = Rotate(M2, -(ro7 + 360 b1) °, D3)
N2' = Rotate(N2, -(ro7 + 360 b1) °, D3)
poly6', c2', d2', e2', f2', g2', h2', i2', j2', k2', l2', m2', n2' = Polygon(C2', D2', E2', F2', G2', H2', I2', J2', K2', L2', M2', N2')
C2'_1 = Rotate(C2, 180°, D3)
D2'_1 = Rotate(D2, 180°, D3)
E2'_1 = Rotate(E2, 180°, D3)
F2'_1 = Rotate(F2, 180°, D3)
G2'_1 = Rotate(G2, 180°, D3)
H2'_1 = Rotate(H2, 180°, D3)
I2'_1 = Rotate(I2, 180°, D3)
J2'_1 = Rotate(J2, 180°, D3)
K2'_1 = Rotate(K2, 180°, D3)
L2'_1 = Rotate(L2, 180°, D3)
M2'_1 = Rotate(M2, 180°, D3)
N2'_1 = Rotate(N2, 180°, D3)
poly6'_1, c2'_1, d2'_1, e2'_1, f2'_1, g2'_1, h2'_1, i2'_1, j2'_1, k2'_1, l2'_1, m2'_1, n2'_1 = Polygon(C2'_1, D2'_1, E2'_1, F2'_1, G2'_1, H2'_1, I2'_1, J2'_1, K2'_1, L2'_1, M2'_1, N2'_1)
tr8: sqrt(b1 - 0.5) 0
z1 = Vector(C2'_1, C2'_1 + (tr8 + 2 b1 - 1) * (P2 - C2'_1))
C2'_1' = Translate(C2'_1, z1)
D2'_1' = Translate(D2'_1, z1)
E2'_1' = Translate(E2'_1, z1)
F2'_1' = Translate(F2'_1, z1)
G2'_1' = Translate(G2'_1, z1)
H2'_1' = Translate(H2'_1, z1)
I2'_1' = Translate(I2'_1, z1)
J2'_1' = Translate(J2'_1, z1)
K2'_1' = Translate(K2'_1, z1)
L2'_1' = Translate(L2'_1, z1)
M2'_1' = Translate(M2'_1, z1)
N2'_1' = Translate(N2'_1, z1)
poly6'_1', c2'_1', d2'_1', e2'_1', f2'_1', g2'_1', h2'_1', i2'_1', j2'_1', k2'_1', l2'_1', m2'_1', n2'_1' = Polygon(C2'_1', D2'_1', E2'_1', F2'_1', G2'_1', H2'_1', I2'_1', J2'_1', K2'_1', L2'_1', M2'_1', N2'_1')
g1 = Vector(U1, Z1)
U1'_2 = Translate(U1, g1)
V1'_3 = Translate(V1, g1)
W1'_3 = Translate(W1, g1)
t1 = Sector(Translate[Circle[U1, V1], g1], V1'_3, W1'_3)
V1'_3' = Rotate(V1'_3, (ro6 + 180 a1 - 90) °, Z1)
W1'_3' = Rotate(W1'_3, (ro6 + 180 a1 - 90) °, Z1)
t2 = Sector(Rotate[Translate[Circle[U1, V1], g1], (ro6 + 180 a1 - 90) °, Z1], V1'_3', W1'_3')
E3 = (7.199999999999999, 7.199999999999999)
F3 = (12, 7.199999999999999)
G3: bo1 E3
H3: bo1 F3
a = Segment(G3, H3)
I3 = (-1.2, -3.5999999999999996)
J3 = (2.1, -3.6333333333333333)
K3: bo2 I
L3: bo2 J3
M3: bo2 I3
b = Segment(M3, L3)
N3 = (-7.133333333333333, 10.466666666666667)
O3 = (16.766666666666666, 10.466666666666667)
P3 = (16.8, 9)
Q3 = (-7.199999999999999, 9)
poly8, n3, o3, p3, q3 = Polygon(N3, O3, P3, Q3)