The heights of two poles standing erect on a flat ground are $6 \, m$ and $11 \, m$. If the distance between their bases is $12 \, m$,find the distance between their tops.

In $\square ABCD$,$\overline{AB} \parallel \overline{CD}$,$M \in \overline{AD}$ and $N \in \overline{BC}$. If $\overline{MN} \parallel \overline{AB}$,prove that $\frac{DM}{MA} = \frac{CN}{NB}$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AB = 2\sqrt{10}$ and $AM = 5$,find $CM$.

In rhombus $ABCD$,$AC = 18$ and $BD = 24$. Find the perimeter of rhombus $ABCD$.

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = x+1$,$MB = x$,$AN = 3x-3$ and $NC = 4x-10$,then $x = \dots$

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.