Answer
Yes, the triangles are similar.
$\triangle JKL ∼ \triangle PQR$
The scale factor is $\frac{2}{1}$ or $2:1$.
Work Step by Step
First, we identify all the pairs of congruent angles:
$\angle K ≅ \angle Q$
$\angle J ≅ \angle P$
$\angle L ≅ \angle R$
Now, let's take a look at the corresponding sides in both triangles:
$\frac{JK}{PQ} = \frac{16}{8}$
Divide the numerator and denominator by their greatest common factor, $8$:
$\frac{JK}{PQ} = 2$
Let's look at $KL$ and $QR$:
$\frac{KL}{QR} = \frac{34}{17}$
Divide the numerator and denominator by their greatest common factor, $17$:
$\frac{KL}{QR} = 2$
Let's look at $LJ$ and $RP$:
$\frac{LJ}{RP} = \frac{30}{15}$
Divide the numerator and denominator by their greatest common factor, $15$:
$\frac{LJ}{RP} = 2$
$\triangle JKL ∼ \triangle PQR$ because all angles are congruent, and all sides are proportional.
The scale factor is $\frac{2}{1}$ or $2:1$.
