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: Compare corresponding sides

Calculate ratios of $\triangle ABC$ sides to $\triangle DEF$ sides:
$\frac{AB}{DE} = \frac{15}{10}$, $\frac{AC}{DF} = \frac{12}{8}$, $\frac{BC}{EF} = \frac{18}{12}$

Step2: Simplify each ratio

$\frac{15}{10} = \frac{3}{2}$, $\frac{12}{8} = \frac{3}{2}$, $\frac{18}{12} = \frac{3}{2}$
All ratios are equal, so $\triangle ABC \sim \triangle DEF$ by SSS similarity.

Step3: Identify scale factor

The scale factor $k$ is the common ratio.

Answer:

$\frac{3}{2}$