Similar Triangles: Comparing Triangles with Sides 6:12 and 2:4

To determine if the triangles are similar, we will use the Side-Side-Side (SSS) similarity criterion, which checks if the corresponding sides of both triangles are proportional.

Let's analyze the given side lengths:
Triangle $\triangle ABC$ has sides $AB = 6$, $BC = 2$, and $AC = 4$.
Triangle $\triangle DEF$ has sides $DE = 12$, $EF = 4$, and $DF = 8$.

Now, calculate the ratios of corresponding sides:

• Ratio for sides $AB$ and $DE$: $\frac{6}{12} = \frac{1}{2}$
• Ratio for sides $BC$ and $EF$: $\frac{2}{4} = \frac{1}{2}$
• Ratio for sides $AC$ and $DF$: $\frac{4}{8} = \frac{1}{2}$

Since all corresponding sides are in the same proportion $\frac{1}{2}$, the triangles satisfy the SSS criterion for similarity.

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

Thus, the answer is Yes.