Answer
$\triangle ABC ∼ \triangle DEF$
The scale factor is $\frac{3}{5}$ or $3:5$.
Work Step by Step
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 $3:5$.
