Similar Triangles Analysis: Compare Triangles with Sides 6:3 and 4:2

To determine if the triangles ABC and DEF are similar, we need to examine the ratios of corresponding sides.

• Side AC (6) corresponds to side DF (3).
• Side BC (4) corresponds to side EF (2).
• Side AB (2) corresponds to side DE (1).

We calculate the ratios of corresponding sides:

• $\frac{AC}{DF} = \frac{6}{3} = 2$
• $\frac{BC}{EF} = \frac{4}{2} = 2$
• $\frac{AB}{DE} = \frac{2}{1} = 2$

All the corresponding side ratios are equal to 2, indicating that the sides of triangle ABC are proportional to the sides of triangle DEF by a common ratio. According to the Side-Side-Side (SSS) similarity criterion, this means the triangles are similar.

Therefore, the triangles are indeed similar. The correct answer is Yes.