Triangles ABC and DBC have the following characteristics:

Given the conditions of the triangles \( \triangle ABC \) and \( \triangle DBC \):

1. \( BC \) is a common side for both triangles.
2. \( \angle ACB \) and \( \angle DCB \) are right angles.
3. \( AC \cong DC \) (the hypotenuses of the right triangles are congruent).

Since we have two right triangles, we can apply the Hypotenuse-Leg (HL) congruence theorem. This theorem states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

In this case:

• Hypotenuse \( AC \) is congruent to hypotenuse \( DC \).
• Leg \( BC \) is the common leg of both triangles.

Therefore, the congruence theorem that can be used to prove \( \triangle ABC \cong \triangle DBC \) is HL.