The length of a diagonal of a square is $6$. Then,its area is............

In $\Delta ABC$,$A-D-B$,$A-E-C$ and $BD = CE$. If $m\angle B = m\angle C$,prove that $\overline{DE} \parallel \overline{BC}$.

If $\triangle ABC \sim \triangle QRP$,$\frac{\operatorname{ar}(\triangle ABC)}{\operatorname{ar}(\triangle QRP)} = \frac{9}{4}$,$AB = 18 \, cm$ and $BC = 15 \, cm$,then $PR$ is equal to (in $cm$):

The perimeter of an equilateral triangle is $18$. Then,the length of its altitude is $\ldots \ldots \ldots$

If $\Delta ABC \sim \Delta MNP$ for the correspondence $ABC \leftrightarrow MNP,$ the perimeter of $\Delta ABC$ is $18$ and the perimeter of $\Delta MNP$ is $27.$ If $AB = 8,$ then $MN = \dots$

In $\Delta ABC$,the correspondences $ABC \leftrightarrow BAC$ and $ABC \leftrightarrow ACB$ are similarities. Then,$\Delta ABC$ is a/an $\ldots \ldots \ldots \ldots$ triangle.