Numbers and triangles

Consider the set $A$ of all triads $(a,b,c)$ such that $a+b>c$, $c+a>b$, $b+c>a$. Let the set of all triangles be $T$. Two elements of $T$ will be said to be the same if both of them are having the same sides. Does there exists a one-one correspondence between the sets $A$ and $T$?

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Yes.$\qquad\quad$ – Brian M. Scott May 24 '12 at 6:36
@Marvis I do not know how to accept answers. Sorry – Primeczar May 24 '12 at 7:02
@BrianM.Scott Hope you can provide a proof to justify your answer. – Primeczar May 24 '12 at 7:03
@Primeczar There is a tick mark on the side of each of the answers. Once you click on them it will turn green which means that you have accepted the answer. You may want to look here (meta.stackexchange.com/questions/5234/…) for more details. Note that you can also up-vote and down-vote answers! – user17762 May 24 '12 at 7:05

You may need to adjust this. $A$ will contain $(2,3,4)$, $(2,4,3)$, $(3,2,4)$, $(3,4,2)$ $(4,2,3)$ and $(4,3,2)$ as distinct elements but the definition of $T$ might treat these as the same.
Another issue to check is showing each side is positive, though for $a$ this follows from $a + b \gt c$ and $c + a \gt b$ and similarly for the other two.