In $\Delta XYZ$,$m\angle Y = 90^{\circ}$ and $\overline{YP}$ is a median. If $YP = 6$,then $XZ = \ldots$

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AC = 25$ and $AM = 16$,then $BM = \dots$

$\Delta XYZ \sim \Delta DEF$ 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 $\Delta ABC$,$m \angle B = 90^{\circ}$. If $AC - BC = 4$ and $BC - AB = 4$,find the lengths of all the sides of $\Delta ABC$.

The length of a diagonal of a square is $6$. Then, the length of its sides is $\ldots \ldots \ldots$ (in $\sqrt{2}$)

In a triangle,if the bisector of an angle bisects the side opposite to that angle,then prove that the triangle is an isosceles triangle.