1. If $a>b>c>0$, then $b>a-c$ is ( ) for $a$, $b$, and $c$ to be the lengths of the sides of a triangle.
(A) a sufficient but not necessary condition
(B) a necessary but not sufficient condition
(C) a sufficient and necessary condition
(D) neither a sufficient nor a necessary condition
-1.C.
The necessity of the condition is obvious.
From $b>a-c$, we get $b+c>a$. Since $a$ is the largest, this ensures that the sum of any two lengths is greater than the third length. Thus, we know the condition is sufficient.