Question

a triangle abc with ac = 12, ab = 8, bc = 6. another triangle edf with ed = 3, df = 4, ef = 6. options: not similar or not necessarily similar; similar: △abc ~ △□ by the select dropdown.

Explanation:

Step1: Find side ratios

For $\triangle ABC$: sides are $AB = 8$, $BC = 6$, $AC = 12$.
For $\triangle EFD$: sides are $EF = 6$, $FD = 4$, $ED = 3$.
Calculate ratios: $\frac{AB}{EF}=\frac{8}{6}=\frac{4}{3}$? No, wait: $\frac{AC}{EF}=\frac{12}{6}=2$, $\frac{AB}{FD}=\frac{8}{4}=2$, $\frac{BC}{ED}=\frac{6}{3}=2$.

Step2: Identify similarity

All corresponding sides are in ratio $2$ (SSS similarity: if $\frac{a}{a'}=\frac{b}{b'}=\frac{c}{c'}$, triangles are similar). So $\triangle ABC \sim \triangle FDE$ (order: $AC$ corresponds to $EF$, $AB$ to $FD$, $BC$ to $ED$).

Answer:

Similar: $\triangle ABC \sim \triangle FDE$ by the SSS (Side - Side - Side) Similarity Criterion.