In $\Delta PQR$ and $\Delta XYZ$,$\angle P \cong \angle X$ and $\angle Q \cong \angle Z$. If $PQ = 9$,$QR = 6$,$PR = 4.5$,and $XY = 7.5$,find $YZ$ and $XZ$.

(A) Given that $\angle P = \angle X$ and $\angle Q = \angle Z$. By $AA$ similarity criterion,$\Delta PQR \sim \Delta XZY$.
Since the triangles are similar,the ratios of their corresponding sides are equal:
$\frac{PQ}{XZ} = \frac{QR}{ZY} = \frac{PR}{XY}$.
Substituting the given values:
$\frac{9}{XZ} = \frac{6}{YZ} = \frac{4.5}{7.5}$.
First,simplify the ratio $\frac{4.5}{7.5} = \frac{45}{75} = \frac{3}{5} = 0.6$.
Now,solve for $XZ$:
$\frac{9}{XZ} = 0.6 \implies XZ = \frac{9}{0.6} = 15$.
Next,solve for $YZ$:
$\frac{6}{YZ} = 0.6 \implies YZ = \frac{6}{0.6} = 10$.
Therefore,$YZ = 10$ and $XZ = 15$.