17-130 Condition A: The sum of the areas of two triangles and two corresponding sides are equal. Condition B: The two triangles are congruent. Then
(A) A is a sufficient and necessary condition for B.
(B) A is a necessary condition for B.
(C) A is a sufficient condition for B.
(D) A is neither a necessary condition nor a sufficient condition for B.
(China High School Mathematics League, 1981)
［Solution］From condition β, condition α can obviously be deduced; however, condition α cannot deduce condition β. For example, in $\triangle A B C$ and $\triangle A^{\prime} B^{\prime} C^{\prime}$, $A B=A^{\prime} B^{\prime}, A C=A^{\prime} C^{\prime}, \angle A=120^{\circ}$, $\angle A^{\prime}=60^{\circ}$, this satisfies condition α, yet these two triangles are not congruent.
Thus, α is a necessary condition for β.
Therefore, the answer is $(B)$.