Which congruence theorem can be used to prove △BDA ≅ △DBC?

To determine which congruence theorem can be used to prove \( \triangle BDA \cong \triangle DBC \), we need to analyze the given information:

1. Shared side: Both triangles share side \( DB \).
2. Right angles: Angles \( CBD \) and \( ADB \) are right angles.
3. Congruent sides: Sides \( CD \) and \( BA \) are congruent.

Given that both are right triangles (due to the right angles), we can apply the Hypotenuse-Leg (HL) theorem. The HL theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

In this case:

• The hypotenuses \( AB \) (in \( \triangle BDA \)) and \( BC \) (in \( \triangle DBC \)) are congruent because both are sides across right angles.
• The sides \( BA \) and \( CD \) are given as congruent.

Thus, the HL theorem can be used to prove that \( \triangle BDA \cong \triangle DBC \).

The answer is: HL.