*A
b/ 
C* 
a\  c
*B
The classical version one learns in school:
A/C (b=0)

 a=c

B
Otherwise, $b$ will have some length that will cover $a$ (at worst), or cancel $a$ (at best).
The two cases are something like:
A
b

c*C
a


B
In this case, it's clear that $a  b < c$ (since $a < c$) and
$a + b = c$. In the other case, we will have:
C
b

A

a
c



B
Where we get $a  b = c$, and $c < a + b$. These are the extremes when the triangle has
zero thickness. In general, because the points are spread out, when we
project everything on the $AB=c$ line, we will get lessthan( <=
)
instead of equals ( =
).