In $\Delta ABC$,$A-D-B$,$A-E-C$ and $\overline{DE} \parallel \overline{BC}$. If $AD = 8$,$AB = 12$ and $AE = 12$,find $EC$.

Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle,write the length of its hypotenuse.
$7 \, cm, 24 \, cm, 25 \, cm$

In $\Delta ABC$,$m\angle B = 90^{\circ}$,$N \in \overline{AB}$ and $M \in \overline{BC}$. Prove that $AM^{2} + CN^{2} = AC^{2} + MN^{2}$.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $AC$. If $AM = 7$ and $CM = 9$,then $BC = \ldots$.

If a line intersects sides $AB$ and $AC$ of a $\Delta ABC$ at $D$ and $E$ respectively and is parallel to $BC$,prove that $\frac{AD}{AB} = \frac{AE}{AC}$ (see Figure).

$A$ triangle whose sides measure ............ is a right-angled triangle.