Answer
Yes, the polygons are similar.
$ABDC ∼ DEFG$
The scale factor is $\frac{2}{3}$ or $2:3$.
Work Step by Step
First, we identify all the pairs of congruent angles:
$\angle A ≅ \angle F ≅ \angle BDC ≅ \angle EDG$
$\angle B ≅ \angle E ≅ \angle C ≅ \angle G$
Now, let's take a look at the corresponding sides in both triangles:
$\frac{AB}{DE} = \frac{4}{6}$
Divide the numerator and denominator by their greatest common factor, $2$:
$\frac{AB}{DE} = \frac{2}{3}$
Let's look at $BD$ and $EF$:
$\frac{BD}{EF} = \frac{4}{6}$
Divide the numerator and denominator by their greatest common factor, $2$:
$\frac{BD}{EF} = \frac{2}{3}$
Let's look at $DC$ and $FG$:
$\frac{DC}{FG} = \frac{4}{6}$
Divide the numerator and denominator by their greatest common factor, $2$:
$\frac{DC}{FG} = \frac{2}{3}$
Let's look at $CA$ and $GD$:
$\frac{CA}{GD} = \frac{4}{6}$
Divide the numerator and denominator by their greatest common factor, $2$:
$\frac{CA}{GD} = \frac{2}{3}$
$ABDC ∼ DEFG$ because all angles are congruent, and all sides are proportional.
The scale factor is $\frac{2}{3}$ or $2:3$.
