In $\Delta ABC$,$A-P-B$,$A-Q-C$ and $\overline{PQ} \parallel \overline{BC}$. If $AP = 2$,$AB = 6$ and $AC = 9$,find $AQ$.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $MA = 8$,$MB = 12$ and $MC = 6$,find $MD$.

$D$ is a point on side $QR$ of $\triangle PQR$ such that $PD \perp QR$. Will it be correct to say that $\triangle PQD \sim \triangle RPD$? Why?

If the measures of the sides of a triangle are $\ldots \ldots \ldots,$ then it is not a right-angled triangle.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BE}$ is a median. If $AB = 3.6$ and $BC = 4.8$,find $BE$.

If $\Delta ABC \sim \Delta PQR$ under the correspondence $ABC \leftrightarrow RPQ$,and $m\angle A = 35^{\circ}$ and $m\angle B = 50^{\circ}$,find $m\angle Q$. (in $^{\circ}$)