In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle P$ and $\angle B \cong \angle Q$. If $\frac{AB}{PQ} = \frac{4}{5}$ and $AC = 20$,find $PR$.

In $\Delta ABC$,$m \angle A = 90^\circ$. If $b = 12$ and $c = 35$,then $a = \ldots$

The length of a diagonal of a square is $8 \sqrt{2}$. Then,its area is $\ldots \ldots \ldots$

$\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow XYZ$. If $AB : XY = 4 : 5$ and $AC = 6$,then $XZ = \ldots$

$A$ line drawn parallel to $\overline{YZ}$ in the plane of $\Delta XYZ$ passes through the midpoint of $\overline{XY}$. Prove that this line bisects $\overline{XZ}$.

In $\Delta ABC$,points $D$ and $E$ lie on $\overline{AB}$ such that $A-D-E-B$ and $AD = EB$. $P \in \overline{AC}$ and $Q \in \overline{BC}$ such that $\overline{DP} \parallel \overline{BC}$ and $\overline{EQ} \parallel \overline{AC}$. Prove that $\overline{PQ} \parallel \overline{AB}$.