## Geometry: Common Core (15th Edition)

$DEGH ∼ PLQR$ The scale factor is $\frac{3}{2}$ or $3:2$.
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 $3:2$.