Can you superimpose the two objects with just 2 transformations? 
What about 1, 2 or 3 reflections?

A = (0.202486439024391, -2.6025980487804903)
B = (-0.050586731707318755, 1.006377560975615)
C = (2.3824864390243894, -0.5225980487804889)
D = (4.46248643902439, -0.4425980487804889)
E = (2.4284376585365823, -2.487866341463417)
poly1, a, b, c, d, e = Polygon(A, B, C, D, E)
F = (-0.48, -2.66)
G = (5.08, -1.84)
u = Vector(F, G)
H = (4.26, 2.96)
I = (9.5, -0.24)
f = Line(H, I)
A' = Translate(A, u)
B' = Translate(B, u)
C' = Translate(C, u)
D' = Translate(D, u)
E' = Translate(E, u)
poly1', a', b', c', d', e' = Polygon(A', B', C', D', E')
A'' = Mirror(A', f)
B'' = Mirror(B', f)
C'' = Mirror(C', f)
D'' = Mirror(D', f)
E'' = Mirror(E', f)
poly1'', a'', b'', c'', d'', e'' = Polygon(A'', B'', C'', D'', E'')

Tool: Tool1
Input: A, B, C, D, E, F, G, E'', B'_1, B''
Output: poly2

C' = Rotate(C, 78*°, E)
E' = Rotate(E, 78*°, E)
u = Vector(F, G)
C'' = Translate(C', u)
f = LineBisector(E, E'')
A'_1 = Mirror(A, f)
C'_1 = Mirror(C, f)
D'_1 = Mirror(D, f)
E'_1 = Mirror(E, f)
g = LineBisector(C'_1, C'')
H = Mirror(A'_1, g)
I = Mirror(B'_1, g)
J = Mirror(C'_1, g)
K = Mirror(D'_1, g)
L = Mirror(E'_1, g)
poly2, h, i, j, k, l = Polygon(H, I, J, K, L)