In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QS}$ is an altitude. If $PS - SR = 10$ and $PQ^2 - QR^2 = 260$,then $PR = \dots$

In $\square ABCD$,$A-Q-B$,$A-P-C$ and $A-R-D$. Given $\overline{PQ} \parallel \overline{BC}$ and $\overline{PR} \parallel \overline{DC}$. Prove that $\frac{AR}{AD} = \frac{AQ}{AB}$.

In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle P$ and $\angle B \cong \angle R$. Then,the correspondence $ABC \leftrightarrow \ldots$ is a similarity.

$A$ $17 \, m$ long ladder leans on a wall such that its lower end rests $8 \, m$ away from the base of the wall. Then,its upper end reaches to the height of $\ldots \ldots \ldots \, m$ on the wall.

The correspondence $ABC \leftrightarrow XYZ$ between $\Delta ABC$ and $\Delta XYZ$ is a similarity. If $4AB = 5XY$ and $BC = 12$,find $YZ$. (in $.6$)

The correspondence $PQR \leftrightarrow ZYX$ between $\Delta PQR$ and $\Delta XYZ$ is a similarity. If $PQ : ZY = 5 : 3$ and $PR = 10$,find $ZX$.