............... is not a condition for the similarity of two triangles.

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

In $\Delta ABC$,$m \angle B = 90^{\circ}$,$\overline{BM}$ is an altitude to the hypotenuse $AC$,and $AM < CM$. If $BM = 6$ and $AC = 13$,find $AB$.

In the given figure,$\angle ADE = \angle AED$ and $\frac{AD}{DB} = \frac{AE}{EC}$. Prove that $\triangle ABC$ is an isosceles triangle.

In the given figure,$OB$ is the perpendicular bisector of the line segment $DE$,$FA \perp OB$,and $FE$ intersects $OB$ at the point $C$. Prove that $\frac{1}{OA} + \frac{1}{OB} = \frac{2}{OC}$.

The length of a diagonal of a square is $5 \sqrt{2}$. Then,the length of its sides is............