Similar Triangles Analysis: Comparing Triangles with Sides 4 and 5 Units

To solve this problem, we'll determine if the triangles $\triangle ABC$ and $\triangle DEF$ are similar using the Side-Side-Side (SSS) similarity criterion.

Step 1: Identify the sides of both triangles:
For $\triangle ABC$, the side lengths are $AB = 5$, $BC = 4$, and $CA = 4$.
For $\triangle DEF$, the side lengths are $DE = 5$, $EF = 4$, and $FD = 4$.

Step 2: Calculate the ratios of the corresponding sides:
$\frac{AB}{DE} = \frac{5}{5} = 1$
$\frac{BC}{EF} = \frac{4}{4} = 1$
$\frac{CA}{FD} = \frac{4}{4} = 1$

Step 3: Verify similarity:
All three ratios are equal, so by the SSS criterion, the triangles are similar.

Therefore, the triangles $\triangle ABC$ and $\triangle DEF$ are similar.