State whether the following statement is true or false:
$(1)$ In $\Delta PQR$,$\angle P = \angle Q = 95^{\circ}$ is possible.

$P$ is a point on the bisector of $\angle ABC$. If the line through $P$,parallel to $BA$,meets $BC$ at $Q$,prove that $\triangle BPQ$ is an isosceles triangle.

In the figure,$AD$ is the bisector of $\angle BAC$. Prove that $AB > BD$.

Prove that the sum of any two sides of a triangle is greater than twice the median with respect to the third side.

Angles of a triangle are in the ratio $2: 4: 3$. The smallest angle of the triangle is (in $^{\circ}$)

In the given figure,in $\Delta PQR$,$\angle Q > \angle R$. $PM \perp QR$ and $PA$ is the bisector of $\angle QPR$. Prove that $\angle APM = \frac{1}{2}(\angle Q - \angle R)$.