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

Is it possible to construct a triangle with lengths of its sides as $4 \, cm, 3 \, cm$ and $7 \, cm$? Give reason for your answer.

$P$ 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.

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

In triangles $ABC$ and $PQR$,$\angle A = \angle Q$ and $\angle B = \angle R$. Which side of $\triangle PQR$ should be equal to side $BC$ of $\triangle ABC$ so that the two triangles are congruent? Give reason for your answer.

Prove that if in two triangles,two angles and the included side of one triangle are equal to two angles and the included side of the other triangle,then the two triangles are congruent.