Congruent Triangles ABC and DEF: Proving Equilateral Properties

To solve this problem, let's go through the steps clearly:

• Step 1: Since triangles $\triangle ABC$ and $\triangle DEF$ are equilateral, each side of these triangles is equal to the other sides of the same triangle.
• Step 2: Moreover, given that $\triangle ABC \cong \triangle DEF$, these triangles are congruent, meaning that the corresponding sides and angles are equal. Therefore, side $AB = DE$, $BC = EF$, and $CA = FD$.

Since every side of $\triangle ABC$ is equal to every corresponding side of $\triangle DEF$, the ratio between any corresponding sides of these triangles is:

$\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD} = 1$

Therefore, all sides have a ratio of $1$, which means that the correct statement is that "The ratio between the sides is equal to 1."

Therefore, the correct choice is choice 4.

Hence, the solution to this problem is: The ratio between the sides is equal to 1.