In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle Q$ and $\angle B \cong \angle R$. Which correspondence between them is a similarity?

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM : MB = 4 : 13$ and $AC = 20.4$,find $AN$.

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 $\overline{PQ} \parallel \overline{AB}$.

$\square ABCD$ is a trapezium in which $\overline{ AD } \| \overline{ BC }, \overline{ AC } \cap \overline{ BD }=\{ P \} .$ If $PD =9, PA =5$ and $PB =7.2,$ then $AC =\ldots \ldots \ldots \ldots$

$\Delta ABC \sim \Delta PQR$ for the correspondence $ABC \leftrightarrow PQR.$ The perimeter of $\Delta ABC$ is $16$ and the perimeter of $\Delta PQR$ is $24.$ If $AB = 6$,find $PQ$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $AB : AC = 24 : 25$. If $BC = 14$,find the perimeter of $\Delta ABC$.