In parallelogram $ABCD$,$AB^{2} + BC^{2} = 260$ and $AC = 18$. Then $BD = \ldots$

$\Delta XYZ \sim \Delta ABC$ for the correspondence $XYZ \leftrightarrow ABC$. If $\frac{XY}{AB} = \frac{3}{5}$,then $\frac{BC}{YZ} = \dots$

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $AC$. If $AB = 7$ and $BC = 24$,find the length of $BM$.

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 $m \angle C = 30^{\circ}$. If $AC = 10$,then $AB = \ldots$

In $\Delta ABC$, $P$ and $Q$ are the midpoints of $\overline{AB}$ and $\overline{AC}$ respectively. If the area of $\Delta APQ = 12 \sqrt{3}$, then the area of $\Delta ABC = \ldots$ (in $\sqrt{3}$)