Triangle ABC is similar to triangle DEF, with vertex A corresponding to D, B to E, and C to F. If AB = 8, BC = 12, and DE = 6, what is the…

Similar triangles have proportional corresponding sides. The correspondence $A \to D$, $B \to E$, $C \to F$ means $AB$ matches $DE$ and $BC$ matches $EF$. The scale factor from $ABC$ to $DEF$ is $\frac{DE}{AB} = \frac{6}{8} = \frac{3}{4}$. Therefore $EF = \frac{3}{4} \times BC = \frac{3}{4} \times 12 = 9$, choice D. Choice A (8) is the length of $AB$, copied from the figure. Choice B (16) results from applying the ratio upside down, $12 \times \frac{4}{3}$. Choice C (10) comes from subtracting: $12 - 2$, since $8 - 6 = 2$. Similarity uses ratios, not differences.