1. Condition A: Two triangles have equal areas and two corresponding sides are equal.
Condition B: Two triangles are congruent.
(A) A is the necessary and sufficient condition for B;
(B) A is the necessary condition for B;
(C) A is the sufficient condition for B;
(D) A is neither the necessary condition nor the sufficient condition for B.
1. (B)

If two triangles are congruent, then their corresponding sides are equal, and their areas are also equal. Therefore, A is a necessary condition for B.

In $\triangle ABC$, $AB \geqslant AC$. M is the midpoint of $BC$, then in $\triangle ABM$ and $\triangle ACM$, $AM=AM, BM=CM, S_{\triangle ABM}=S_{\triangle ACM}$. However, $\triangle ABM$ and $\triangle ACM$ are not congruent, so A is not a sufficient condition for B.