If $AB = QR$,$BC = PR$,and $CA = PQ$,then

Two sides of a triangle are of lengths $5\, cm$ and $1.5\, cm$. The length of the third side of the triangle cannot be (in $cm$):

In $\Delta ABC$,$AB = 6 \text{ cm}$ and $BC = 9 \text{ cm}$,then $AC < \dots \text{ cm}$.

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 $MN$.

In $\Delta ABC$,the bisectors of $\angle B$ and $\angle C$ intersect at $P$. $A$ line drawn through $P$ and parallel to $BC$ intersects $AB$ at $X$ and $AC$ at $Y$. Prove that $XY = XB + YC$.

In $\Delta ABC$,$\angle B = 50^{\circ}$ and $\angle C = 85^{\circ}$,then $AB$ $\dots$ $AC$.