Question

verify that $\triangle abc \sim \triangle def$. find the scale factor of $\triangle abc$ to $\triangle def$.$\triangle abc$: $bc = 18$, $ab = 15$, $ac = 12LXB0k = \square$

Explanation:

Step1: Verify similarity via side ratios

Calculate ratios of corresponding sides:
$\frac{AB}{DE} = \frac{15}{10} = \frac{3}{2}$, $\frac{AC}{DF} = \frac{12}{8} = \frac{3}{2}$, $\frac{BC}{EF} = \frac{18}{12} = \frac{3}{2}$
All ratios are equal, so $\triangle ABC \sim \triangle DEF$.

Step2: Identify scale factor (ABC to DEF)

The scale factor $k$ is the ratio of corresponding sides of $\triangle ABC$ to $\triangle DEF$.
$k = \frac{AB}{DE} = \frac{15}{10} = \frac{3}{2}$

Answer:

$\frac{3}{2}$