In $\Delta ABC$, $\angle B = \angle C$, $AB = 5 \text{ cm}$, and $BC = 8 \text{ cm}$. Then, the perimeter of $\Delta ABC$ is: (in $\text{ cm}$)

"If two sides and an angle of one triangle are equal to two sides and an angle of another triangle,then the two triangles must be congruent." Is the statement true? Why?

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.

$PQRS$ is a parallelogram. If the two diagonals are equal,find the measure of $\angle PQR$. (in $^{\circ}$)

In $\Delta XYZ$,$XY = XZ$ and $\angle X = 80^{\circ}$,then $\angle Y = \ldots$ (in $^{\circ}$)

In $\Delta PQR$,$PQ = PR$. Prove that $\angle R = \angle Q$.