In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 8$ and $CM = 2$,then $BM = \ldots$

In $\Delta XYZ$,$X-P-Y$,$X-Q-Z$ and $\overline{PQ} \parallel \overline{YZ}$. If $XY = 5.6$,$XP = 1.4$ and $XZ = 7.2$,find $XQ$.

In $\square XYZW$,$\overline{XY} \parallel \overline{ZW}$ and $\overline{XZ} \cap \overline{YW} = \{P\}$. If $PX = 3x - 1$,$PY = 2x + 1$,$PZ = 5x - 3$,and $PW = 6x - 5$,find the value of $x$.

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

If in the figure, $O$ is the point of intersection of two chords $AB$ and $CD$ such that $OB = OD$, then triangles $OAC$ and $ODB$ are

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = 2$,$MB = 5$ and $MN = 4$,find $BC$.