Similar Triangles: Comparing ABC (7,5,4) and DEF (7,5,3) Triangles

To determine whether the triangles are similar, we will use the Side-Side-Side (SSS) criterion for similarity. According to this criterion, triangles are similar if the ratios of their corresponding sides are equal.

We have two triangles: $\triangle ABC$ with sides 7, 5, and 4, and $\triangle DEF$ with sides 7, 5, and 3.

We will calculate the ratios of the corresponding sides:

• For sides $AB$ and $DE$: $\frac{AB}{DE} = \frac{7}{7} = 1$
• For sides $BC$ and $EF$: $\frac{BC}{EF} = \frac{5}{5} = 1$
• For sides $AC$ and $DF$: $\frac{AC}{DF} = \frac{4}{3}$

From the calculations, we observe that two of the side ratios are equal to 1, but the third ratio $\frac{4}{3}$ does not match the others. Thus, the side ratios are not all identical, meaning the triangles are not similar according to the SSS criterion.

Therefore, the triangles $\triangle ABC$ and $\triangle DEF$ are not similar.