Question

multiple choice (single select) 13 points given that △abc ~ △def, ab:de = 4:1, ac = 8, then df is _____. a 18 b 2 c 54 d $\frac{2}{3}$

Explanation:

Step1: Recall property of similar triangles

For similar triangles $\triangle ABC\sim\triangle DEF$, the ratios of corresponding - sides are equal, i.e., $\frac{AB}{DE}=\frac{AC}{DF}$.

Step2: Substitute given values

We know that $\frac{AB}{DE} = \frac{4}{1}$ and $AC = 8$. Substituting into $\frac{AB}{DE}=\frac{AC}{DF}$, we get $\frac{4}{1}=\frac{8}{DF}$.

Step3: Solve for $DF$

Cross - multiply: $4\times DF=8\times1$. Then $DF=\frac{8}{4}=2$.

Answer:

B. 2