Proof that When all the sides of two triangles are congruent, the angles of those triangles must also be congruent (Side-Side-Side Congruence) I am studying triangle congruence. It is a very basic subject and maybe because of that I am having a very hard time finding more rigorous explanations. I am specifically interested in the Side-Side-Side Congruence.
I know that "When all the sides of two triangles are congruent, the angles of those triangles must also be congruent". But I can not find a proof for that. Can anyone provide me a proof?
 A: Euclid, Book I, Proposition 8:

If two triangles have the two sides equal to two sides
respectively, and also have the base equal to the base, then they also
have the angles equal which are contained by the equal straight lines.



Let ABC and DEF be two triangles having the two sides AB and AC equal
to the two sides DE and DF respectively, namely AB equal to DE and AC
equal to DF, and let them have the base BC equal to the base EF.
I say that the angle BAC also equals the angle EDF.
If the triangle ABC is applied to the triangle DEF, and if the point B
is placed on the point E and the straight line BC on EF, then the
point C also coincides with F, because BC equals EF.
Then, BC coinciding with EF, therefore BA and AC also coincide with ED
and DF, for, if the base BC coincides with the base EF, and the sides
BA and AC do not coincide with ED and DF but fall beside them as EG
and GF, then given two straight lines constructed on a straight line
and meeting in a point, there will have been constructed on the same
straight line and on the same side of it, two other straight lines
meeting in another point and equal to the former two respectively,
namely each to that which has the same end with it.
But they cannot be so constructed.
Therefore it is not possible that, if the base BC is applied to the
base EF, the sides BA and AC do not coincide with ED and DF. Therefore
they coincide, so that the angle BAC coincides with the angle EDF, and
equals it.
Therefore if two triangles have the two sides equal to two sides
respectively, and also have the base equal to the base, then they also
have the angles equal which are contained by the equal straight lines.
Q.E.D.

http://aleph0.clarku.edu/~djoyce/elements/bookI/propI8.html
A: The angles of a triangle are uniquely determined by the law of cosines if you know all the side lengths. Have a look at this forum post.
So, two triangles with equal side lengths also have have identical angles.
