In $\Delta ABC$,$A-D-B$,$A-E-C$ and $\overline{DE} \parallel \overline{BC}$. If $AB:AC = 3:4$,which of the following holds true?

Is the triangle with sides $25 \, cm$,$5 \, cm$,and $24 \, cm$ a right triangle? Give reasons for your answer.

In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle R$ and $\angle B \cong \angle P$. If $AB = 6$,$BC = 8$ and $PR = 9$,then $PQ = \ldots$

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$ and $\overline{AC} \cap \overline{BD} = \{M\}$. If $MA = 3x - 19$,$MB = x - 3$,$MC = x - 5$,and $MD = 3$,find the value of $x$.

In $\Delta PQR$,$\angle P$ is a right angle and $\overline{PX}$ is an altitude. If $QX = 4$ and $RX = 5$,then $PQ = \ldots \ldots$

In $\Delta DEF, m \angle D = 90^{\circ}$. If $EF = 6$ and $DF = 4$,then $DE = \dots$