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
Answer ( )
(B)
I. Multiple Choice Question
1.【Analysis and Solution】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 $\triangle A B C$, $A B \geqslant A C . M$ is the midpoint of $B C$, then in $\triangle A B M$ and $\triangle A C M$, $A M=A C, B M=C M, S_{\triangle A B M}=S_{\triangle A C M}$.
However, $\triangle A B M$ and $\triangle A C M$ are not congruent, so A is not a sufficient condition for B.