The problem provides a geometric proof. We are given that $DB$ bisects $\angle ABC$ and $\angle A \cong \angle C$. We need to prove that $\triangle ABD \cong \triangle CBD$. The first step of the proof is already provided, stating the givens. We need to determine the second statement.

1. Problem Description

The problem provides a geometric proof. We are given that $DB$ bisects $\angle ABC$ and $\angle A \cong \angle C$. We need to prove that $\triangle ABD \cong \triangle CBD$. The first step of the proof is already provided, stating the givens. We need to determine the second statement.

2. Solution Steps

Since $DB$ bisects $\angle ABC$, this means $\angle ABD \cong \angle CBD$. So this is our next statement.

Step 1: $DB$ bisects $\angle ABC$ and $\angle A \cong \angle C$ (Given)

Step 2: $\angle ABD \cong \angle CBD$ (Definition of angle bisector)

3. Final Answer

$\angle ABD \cong \angle CBD$