Question

$\triangle abc \cong \triangle dbc$, find $dc$.
$dc = ?$

Explanation:

Step1: Recall congruent triangles property

Since $\triangle ABC \cong \triangle DBC$, corresponding sides are equal. In congruent triangles, corresponding sides $AC$ and $DC$? Wait, no, wait. Wait, actually, in $\triangle ABC$ and $\triangle DBC$, the corresponding sides: $AB$ corresponds to $DB$, $BC$ is common, and $AC$ corresponds to $DC$? Wait, no, let's check the sides. Wait, $AC$ is 7, and since $\triangle ABC \cong \triangle DBC$, then $AC = DC$? Wait, no, wait, $AB = DB = 10$, and $AC$ and $DC$: Wait, actually, in the diagram, $AC$ is 7, and since $\triangle ABC \cong \triangle DBC$, the corresponding side to $AC$ is $DC$? Wait, no, maybe $AC$ and $DC$: Wait, $\triangle ABC \cong \triangle DBC$, so $AC = DC$? Wait, no, wait, $AC$ is 7, so $DC$ should be equal to $AC$? Wait, no, wait, let's see: in $\triangle ABC$ and $\triangle DBC$, $AC$ and $DC$: Wait, $AC$ is 7, so $DC = AC = 7$? Wait, is that correct? Wait, because when two triangles are congruent, corresponding parts are equal. So $AC$ corresponds to $DC$, so $AC = DC$. So $DC = 7$. Wait, but let's confirm. $AB = DB = 10$, $BC$ is common, and $AC = DC$. So yes, because $\triangle ABC \cong \triangle DBC$, so $AC = DC$. Since $AC = 7$, then $DC = 7$.

Step2: Apply congruent triangles

Given $\triangle ABC \cong \triangle DBC$, by the property of congruent triangles, corresponding sides are equal. So $AC = DC$. We know $AC = 7$, so $DC = 7$.

Answer:

7