When does Angle Side Side work?

D E and F are constructed to correspond with triangle ABC via "Angle-Side-Side".  In other words, they share two congruent sides and a non-included angle.

Angles D and A are congruent

Segments DE and AB are congruent

Segments EF and BC are congruent.

When does Angle-Side-Side "work" as a congruency shortcut?
When does it not work?  
What happens when it does not work?

A

#1

A

#2

A

#4

A

#3

A

#5

When does Angle-Side-Side “work”?

Show Sample Triangles

You may drag points A, B, C, triangle ABC, and point F.

B = (1.9960112325380281, 5.951172123037243)
A = (-1.0288140876759742, 3.998253874710424)
C = (1.0088284744072384, 2.002441090514091)
poly1, c, a, b = Polygon(A, B, C)
D = (7.220930761319635, 4.500059101069962)
f = Circle(D, c)
d = Ray(D, Vector[A, B])
E = Intersect(f, d, 1)
j = Line(D, E)
g = Circle(E, a)
I, J = Intersect(g, j)
G, H = Intersect(g, d)
u = Vector(A, D)
e = Ray(D, Vector[A, C])
k = CircleArc(E, I, J)
F = Point(k)
h = Segment(E, F)
i = Segment(D, E)
F_2, F_1 = Intersect(g, e)
poly2, f_1, d_3, e_1 = Polygon(D, E, F_1)
d_1 = Distance(F, F_1)
d_2 = Distance(F, F_2)
poly3, f_2, d_4, e_2 = Polygon(D, E, F_2)
α = Angle(C, A, B)
β = Angle(F_1, D, E)
K = (-2, 10)
L = (0, 13)
M = (2, 11)
poly4, m, k_1, l = Polygon(K, L, M)
N = (-2, 6)
O = (1, 8)
P = (1, 6)
poly5, p, n, o = Polygon(N, O, P)
N' = Rotate(N, 30*°, N)
O' = Rotate(O, 30*°, N)
P' = Rotate(P, 30*°, N)
poly5', p', n', o' = Polygon(N', O', P')
Q = (-1, 4)
R = (2, 6)
S = (1, 2)
poly6, s, q, r = Polygon(Q, R, S)
T = (2, 7)
U = (3, 9)
V = (4, 7)
poly7, v, t, u_1 = Polygon(T, U, V)
W = (4, 11)
Z = (7, 11)
A_1 = (7, 9)
poly8, a_1, w, z_1 = Polygon(W, Z, A_1)
W' = Rotate(W, 20*°, W)
Z' = Rotate(Z, 20*°, W)
B_1 = Rotate(A_1, 20*°, W)
poly8', b_1, w', z' = Polygon(W', Z', B_1)
c_1 = true