In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude. If $AB = \sqrt{10}$ and $AM = 2.5$,then $MC = \ldots$

In parallelogram $ABCD$,$P$ is a point on side $BC$. The line segment $DP$ intersects the extension of side $AB$ at point $L$. Prove that: $(1) \frac{DP}{PL} = \frac{DC}{BL}$ and $(2) \frac{DL}{DP} = \frac{AL}{DC}$.

.......... are not the measures of sides of a right-angled triangle.

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

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 $BM = \dots$

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB : AC = 3 : 4$ and $BC = 14$,find $BD$.