In $\Delta ABC$,$\angle B$ is a right angle. Then,according to Pythagoras' theorem,$\ldots \ldots \ldots$ holds good.

$O$ is the point of intersection of the diagonals $AC$ and $BD$ of a trapezium $ABCD$ with $AB \parallel DC$. Through $O$,a line segment $PQ$ is drawn parallel to $AB$ meeting $AD$ in $P$ and $BC$ in $Q$. Prove that $PO = QO$.

In triangles $ABC$ and $DEF$,$\angle B = \angle E$,$\angle F = \angle C$ and $AB = 3 DE$. Then,the two triangles are

In $\Delta PQR$,$m \angle Q = 90^{\circ}$ and $\overline{QM}$ is an altitude to the hypotenuse $PR$. If $QR = 9$ and $PR = 13.5$,find $RM$.

In rhombus $ABCD$,$AC = 16$ and $BD = 30$. Find its perimeter.

In $\Delta ABC$ and $\Delta PQR$,$\angle A \cong \angle R$ and $\angle B \cong \angle P$. If $AB = 6$,$BC = 8$ and $PR = 9$,then $PQ = \ldots$