Question

what additional information do you need to prove △abc ≅ △def by sas?
△abc with sides ab and bc marked with one - dash and two - dashes respectively. △def with sides de and ef marked with one - dash and two - dashes respectively.
∠cab ≅ ∠fde
∠bca ≅ ∠efd
∠abc ≅ ∠def

Explanation:

To prove $\triangle ABC\cong\triangle DEF$ by SAS (Side - Angle - Side) congruence criterion, we need two pairs of corresponding sides to be congruent and the included angle between them to be congruent. From the markings on the triangles, we can see that two pairs of sides are already congruent. We need the included angles of those sides to be congruent. In $\triangle ABC$ and $\triangle DEF$, the included angles for the marked sides are $\angle ABC$ and $\angle DEF$.

Answer:

$\angle ABC\cong\angle DEF$