In triangles $ABC$ and $DEF$,$AB = FD$ and $\angle A = \angle D$. The two triangles will be congruent by the $SAS$ axiom if:

$ABCD$ is a quadrilateral such that diagonal $AC$ bisects the angles $A$ and $C.$ Prove that $AB = AD$ and $CB = CD.$

In $\Delta ABC$,$AB = 9 \, \text{cm}$ and $BC = 12 \, \text{cm}$. If $x < \text{perimeter of } \Delta ABC < y$,then find the values of $x$ and $y$.

In the figure,$PQ > PR$ and $QS$ and $RS$ are the bisectors of $\angle Q$ and $\angle R$,respectively. Show that $SQ > SR$.

State whether each of the following statements is true or false:
$(1)$ In $\Delta ABC$ and $\Delta PQR$,$AB = PQ$,$BC = PR$ and $\angle B = \angle P$,then $\Delta ABC \cong \Delta PQR$.
$(2)$ The exterior angles at two vertices of any triangle cannot both be acute.

$\angle ACD$ is an exterior angle of $\Delta ABC$. If $AB = AC$ and $\angle B = 70^{\circ}$,then $\angle ACD = \dots$ (in $^{\circ}$)