To determine the congruence between the triangles, we compare their side lengths. Given information: For $\triangle ABC$: $AB = 5 \text{ cm}$ $AC = 8 \text{ cm}$ $BC = 4 \text{ cm}$ For $\triangle DBC$: $BD = 8 \text{ cm}$ $CD = 5 \text{ cm}$ $BC = 4 \text{ cm}$ (This side is common to both triangles) Step 1: Compare the corresponding sides. Let's list the sides of $\triangle ABC$ and try to match them with the sides of $\triangle DCB$. Side $AB = 5 \text{ cm}$ in $\triangle ABC$. Side $DC = 5 \text{ cm}$ in $\triangle DCB$. So, $AB = DC$. Side $BC = 4 \text{ cm}$ in $\triangle ABC$. Side $CB = 4 \text{ cm}$ in $\triangle DCB$. So, $BC = CB$. Side $AC = 8 \text{ cm}$ in $\triangle ABC$. Side $DB = 8 \text{ cm}$ in $\triangle DCB$. So, $AC = DB$. Step 2: Determine the congruence criterion. Since all three corresponding sides of $\triangle ABC$ are equal to the three corresponding sides of $\triangle DCB$, the triangles are congruent by the SSS (Side-Side-Side) congruence criterion. Step 3: Write the correct congruence statement. To write the congruence statement, we need to match the vertices correctly based on the equal sides: Since $AB = DC$, vertex A corresponds to vertex D, and vertex B corresponds to vertex C. Since $BC = CB$, vertex B corresponds to vertex C, and vertex C corresponds to vertex B. Since $AC = DB$, vertex A corresponds to vertex D, and vertex C corresponds to vertex B. Combining these, we get the correspondence: A $\leftrightarrow$ D B $\leftrightarrow$ C C $\leftrightarrow$ B Therefore, the correct congruence statement is $\triangle ABC \cong \triangle DCB$. Step 4: Check the given options. (1) $\triangle ABC \cong \triangle DBC$, by SAS - Incorrect vertex correspondence and criterion. (2) $\triangle ABC \cong \triangle DCB$, by SAS - Incorrect criterion. (3) $\triangle ABC \cong \triangle DBC$, by SSS - Incorrect vertex correspondence. (4) $\triangle ABC \cong \triangle DCB$, by SSS - Correct vertex correspondence and criterion. The final answer is $\boxed{\text{4}}$.