help with trying to prove why having two sides and any angle is insufficent proof for congruence. t The author challenges the reader to prove why two sides and any angle is insufficent proof by constructing two triangles with two 1 cm sides and one 45 degree angle. I tried to prove this using the sine rule setting it out how the author proves the other theorem e.g. equating two equations for c and showing that since they equal 0 c=c and so all the sides in the triangle are the same thus the angles are the same so the triangles are congruent. 


Here is how i tried to prove it a=1 b=1 and c is unknown.
  sinA=45
so (1/sin45)=(1/sinb)=(c/sinc)
(sinb/sin45-1)=(c/sinc)
((sinc)(sina)/(sin45))-1=c
  ?
since there are two equal triangles c=c
((sinc)(sina)/(sin45))-1=((sinc)(sina)/(sin45))-1

solving this gives 0 which means that c is equal to c meaning that the triangles are congruent. Any help would be appreciated.

Given the green side, the red side, and the blue angle, there are two triangles possible:
$\hspace{2cm}$

It has been pointed out that the example in the book is for two sides of $1$ and an angle of $45^\circ$. Unfortunately with those values, the family of examples I tried to illustrate above won't work. Below is what I guess they must be going for, although I don't think this is a good counterexample since you are usually given what side the angle opposes.
$\hspace{8mm}$
