## Geometry: Common Core (15th Edition)

$\triangle ABC ∼ \triangle DEF$ The scale factor is $\frac{3}{5}$ or $3:5$.
Here, we have two equilateral triangles, so any angle on one triangle will correspond to any angle on the other triangle. First, we identify all the pairs of congruent angles: $\angle A ≅ \angle D$ $\angle B ≅ \angle E$ $\angle C ≅ \angle F$ Now, let's take a look at the corresponding sides in both triangles: $\frac{AB}{DE} = \frac{9}{15}$ Divide the numerator and denominator by their greatest common factor, $3$: $\frac{AB}{DE} = \frac{3}{5}$ Let's look at $BC$ and $EF$: $\frac{BC}{EF} = \frac{9}{15}$ Divide the numerator and denominator by their greatest common factor, $3$: $\frac{BC}{EF} = \frac{3}{5}$ Let's look at $CA$ and $FD$: $\frac{CA}{FD} = \frac{9}{15}$ Divide the numerator and denominator by their greatest common factor, $3$: $\frac{CA}{FD} = \frac{3}{5}$ $\triangle ABC ∼ \triangle DEF$ because all angles are congruent, and all sides are proportional. The scale factor is $\frac{3}{5}$ or $3:5$.