What additional information is needed to show that △ABC ≅ △DEF by ASA?There are two right angle triangles, triangle ABC and Triangle EDF. Angle BAC is congruent to angle EDF, angle ABC is congruent to angle DEF.

For the triangle congruence postulate ASA to apply between two triangles.
The corresponding angles should be congruent and the side between them should be congruent too:
If the corresponding angles for each triangle are equal:
∠A=∠D
∠B=∠E
The side that links both angles in each triangle should be equal to:
Angles ∠A and ∠B share the leg AB
Angles ∠D and ∠E share the leg DE
For the postulate Angle-Side-Angle it must apply that these sides are equal: AB=DE
The correct option is A.