CONGRUENCE OF TRIANGLES

CORRESPONDING PARTS OF THE TRIANGLES-

1. CORRESPONDING SIDES

AC↔DF⁼2.54
CB↔FG⁼2.85
BA↔GD⁼3.22

2.CORRESPONDING ANGLES-

∠H↔∠J⁼45°
∠U↔∠Y⁼67.5°
∠I↔∠K⁼⁼67.5°

CRITERIA FOR CONGRUENCE OF TRIANGLES

SSS CONGRUENCE CRITERION-

ΔLNO≅ΔPQR

SideOL=Side RP=3.51
Side LN=Side PQ=5
Side NO=SideQR=3.68

SAS CONGRUENCE CRITERION-

ΔSTO≅ΔWZL

Side ST↔Side WZ⁼4
Side SV↔Side WL⁼5
∠ S↔∠  W=47.4

ASA CONGRUENCE CRITERIAN-

ΔABC≅ΔEGF

∠ A↔∠ E=50°
Side AB↔Side EG⁼4
∠ B↔∠G⁼65°

RHS CONGRUENCE CRITERIAN-

90°

ΔDEH≅ΔIJK

90°

∠ D↔∠I⁼90°
Side HE↔Side KJ=5
Side ED↔Side JI=4

A = (0.04, 1.22)
B = (3.26, 1.28)
C = (1.36, 3.4)
t1, c_1, a_1, b_1 = Polygon(A, B, C)
D = (6.98, 1.36)
E_2 = Point(Circle[D, 3.22])
f_1 = Segment(D, E_2)
F = (8.32, 3.52)
G = Point(Circle[F, 2.85])
g = Segment(F, G)
h = Segment(F, D)
H = (-0.32, -3.64)
I = (2.54, -3.64)
i = Segment(H, I)
U = Rotate(I, 45°, H)
a_2 = Angle(I, H, U)
j = Segment(U, H)
k = Segment(U, I)
b_2 = Angle(H, U, I)
c = Angle(U, I, H)
J = (6.4, -3.54)
K = Point(Circle[J, 2.86])
l = Segment(J, K)
Y = Rotate(K, 45°, J)
d = Angle(K, J, Y)
m = Segment(J, Y)
n = Segment(Y, K)
e = Angle(J, Y, K)
f = Angle(Y, K, J)
L = (-0.64, -9.16)
M = Point(Circle[L, 5])
p = Segment(L, M)
N = Point(Circle[L, 5])
q = Segment(L, N)
O = (1.74, -6.58)
r = Segment(O, L)
s = Segment(O, N)
P = (9.24, -9.04)
Q = Point(Circle[P, 5])
t = Segment(P, Q)
R = Point(Circle[P, 3.51])
g_1 = Segment(P, R)
h_1 = Segment(R, Q)
S = (-0.64, -13.78)
T = Point(Circle[S, 4])
i_1 = Segment(S, T)
V = Point(Circle[S, 5])
j_1 = Segment(S, V)
α = Angle(T, S, V)
k_1 = Segment(V, T)
W = (7.38, -13.74)
Z = Point(Circle[W, 4])
l_1 = Segment(W, Z)
L_2 = Point(Circle[W, 5])
m_1 = Segment(W, L_2)
n_1 = Segment(L_2, Z)
β = Angle(Z, W, L_2)
A_1 = (-0.62, -19.84)
B_1 = Point(Circle[A_1, 4])
p_1 = Segment(A_1, B_1)
C_1 = Rotate(B_1, 50°, A_1)
a = Angle(B_1, A_1, C_1)
q_1 = Segment(A_1, C_1)
r_1 = Segment(C_1, B_1)
b = Angle(C_1, B_1, A_1)
E = (7.9, -19.62)
G_1 = Point(Circle[E, 4])
s_1 = Segment(E, G_1)
F_1 = Rotate(G_1, 50°, E)
t_1 = Segment(E, F_1)
d_1 = Segment(F_1, G_1)
ζ = Angle(F_1, G_1, E)
γ = Angle(G_1, E, F_1)
D_1 = (-1.16, -26.38)
E_1 = Point(Circle[D_1, 4])
e_1 = Segment(D_1, E_1)
H_1 = Point(Circle[E_1, 5])
f_2 = Segment(E_1, H_1)
g_2 = Segment(H_1, D_1)
δ = Angle(E_1, D_1, H_1)
I_1 = (7.7, -26.3)
J_1 = Point(Circle[I_1, 4])
h_2 = Segment(I_1, J_1)
K_1 = Point(Circle[J_1, 5])
i_2 = Segment(J_1, K_1)
j_2 = Segment(K_1, I_1)
ε = Angle(J_1, I_1, K_1)