$\Delta ABC \sim \Delta XYZ$ for the correspondence $ABC \leftrightarrow XYZ$. If $AB : XY = 4 : 5$ and $AC = 6$,then $XZ = \ldots$

The correspondence $ABC \leftrightarrow QPR$ between $\Delta ABC$ and $\Delta PQR$ is a similarity. If $m \angle A : m \angle B : m \angle C = 15 : 8 : 7$,find the measures of all the angles of $\Delta PQR$.

In $\Delta PQR$,the bisector of $\angle P$ intersects $\overline{QR}$ at $S$. If $PQ = 8$,$QS = 5.6$ and $QR = 12.6$,find $PR$.

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.

$\square ABCD$ is a square. If its perimeter is $40$, find $AC + BD$. (in $\sqrt{2}$)

If $\triangle ABC \sim \triangle EDF$ and $\triangle ABC$ is not similar to $\triangle DEF$,then which of the following is not true?