In $\Delta ABC$ and $\Delta PQR$,if $\angle B = \angle P = 90^{\circ}$,$AC = RQ$,and $AB = RP$,then $\Delta ABC \cong \Delta \ldots \ldots \ldots$

In $\Delta ABC$,$AD$ is a median. Prove that $AB + AC > 2AD$.

State whether the following statement is true or false:
$(1)$ $\angle ABD$ and $\angle ACE$ are the exterior angles of $\Delta ABC$. If $\angle ABD = 110^{\circ}$ and $\angle ACE = 130^{\circ}$,then $AB > AC$.

If $\Delta PRQ \cong \Delta ZXY,$ then in $\Delta XYZ,$ which angle is equal to $\angle R$?

$Q$ is a point on the side $SR$ of a $\triangle PSR$ such that $PQ = PR$. Prove that $PS > PQ$.

In $\Delta ABC$,$AB = 9 \, \text{cm}$ and $BC = 12 \, \text{cm}$. If $x < \text{perimeter of } \Delta ABC < y$,then find the values of $x$ and $y$.