Two pairs of sides and the included angle are congruent.
At least two pairs of congruent angles and one pair of congruent corresponding sides.
Of the four options, A-D, only three of them are viable theorems for claiming congruence.
B.& HL ≅
C.& SAS ≅
D.& SSS ≅
Of these three, B requires right triangles. From the diagram, we see that there are no indication of the triangles being right triangles, and therefore to claim congruence we have to use either SAS ≅ or SSS ≅.
We also see that the triangles share a side. Therefore, we know that this side is congruent by the Reflexive Property of Congruence.
We can claim congruence by the AAS (Angle-Angle-Side) Congruence Theorem. However, this is not represented in either of the options. Therefore, the correct option is E.
