In $\Delta ABC$ and $\Delta PQR$,if $\angle B = \angle P = 90^{\circ}$,$AC = RQ$,and $AB = RP$,then $\Delta ABC \cong \Delta \ldots \ldots \ldots$

In $\Delta ABC$,$AB = 8 \text{ cm}$ and $BC = 10 \text{ cm}$. Then the perimeter of $\Delta ABC$ is less than how many centimeters?

$PL, QM$ and $RN$ are the altitudes of $\Delta PQR$. If $PL = QM = RN$,then by $AAS$ criterion of congruence,prove that $\Delta PQR$ is an equilateral triangle.

In $\Delta ABC$,$AD$,$BE$,and $CF$ are its medians. Prove that $AB + BC + CA > AD + BE + CF$.

In the given figure,$PQ = PR$ and $\angle Q = \angle R$. Prove that $\triangle PQS \cong \triangle PRT$.

In the given figure,$AM$ and $BN$ are both perpendicular to $AB$. $MN$ intersects $AB$ at $P$. Also,$P$ is the midpoint of $AB$. Prove that $AM = BN$ and $P$ is the midpoint of $MN$.