Answer
$DEGH ∼ PLQR$
The scale factor is $\frac{3}{2}$ or $3:2$.
Work Step by Step
First, we identify all the pairs of congruent angles:
$\angle E ≅ \angle L$
$\angle H ≅ \angle R$
$\angle D ≅ \angle P$
$\angle G ≅ \angle Q$
Now, let's take a look at the corresponding sides in both triangles:
$\frac{DE}{PL} = \frac{18}{12}$
Divide the numerator and denominator by their greatest common factor, $6$:
$\frac{DE}{PL} = \frac{3}{2}$
Let's look at $DH$ and $PR$:
$\frac{DH}{PR} = \frac{24}{16}$
Divide the numerator and denominator by their greatest common factor, $8$:
$\frac{DH}{PR} = \frac{3}{2}$
Let's look at $HG$ and $RQ$:
$\frac{HG}{RQ} = \frac{24}{16}$
Divide the numerator and denominator by their greatest common factor, $8$:
$\frac{HG}{RQ} = \frac{3}{2}$
Let's look at $EG$ and $LQ$:
$\frac{EG}{LQ} = \frac{12}{8}$
Divide the numerator and denominator by their greatest common factor, $4$:
$\frac{EG}{LQ} = \frac{3}{2}$
$DEGH ∼ PLQR$ because all angles are congruent, and all sides are proportional.
The scale factor is $\frac{3}{2}$ or $3:2$.
