In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle P$ and $\angle B \cong \angle R$. If $AB = 8$,$PQ = 7.5$ and $AC = 6$,find $PR$.

$\Delta XYZ \sim \Delta DEF$ for the correspondence $XYZ \leftrightarrow DEF$. If $m \angle X = 50^{\circ}$ and $m \angle Y = 75^{\circ}$,then $m \angle F = \dots$ (in $^{\circ}$)

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is a median. If $AC = 20$,then $BM = \ldots$

The ratio of corresponding sides of two similar triangles is $4:9$. Then,the ratio of their areas is $\ldots \ldots \ldots \ldots$

In $\Delta XYZ$,$m\angle Y = 90^{\circ}$ and $\overline{YM}$ is an altitude to the hypotenuse $\overline{XZ}$. If $XM = \sqrt{12}$ and $ZM = \sqrt{3}$,find $YM$.

In $\Delta PQR$,$P-X-Q$,$P-Y-R$ and $\overline{XY} \parallel \overline{QR}$. If $PX = 3$,$PQ = 8$ and $PY = 4.2$,find $YR$.