In $\Delta ABC$,$AB = AC$ and $\angle C = 75^{\circ}$,then find $\angle B$. (in $^{\circ}$)

In the given figure,$BA \perp AC$ and $DE \perp DF$ such that $BA = DE$ and $BF = EC$. Show that $\triangle ABC \cong \triangle DEF$.

Bisectors of the angles $B$ and $C$ of an isosceles triangle $ABC$ with $AB = AC$ intersect each other at $O$. Show that the external angle adjacent to $\angle ABC$ is equal to $\angle BOC$.

In $\Delta ABC$,$AB = AC$ and $AD$ is an altitude to the base $BC$. Prove that $D$ is the midpoint of $BC$.

$D$ is any point on side $AC$ of a $\triangle ABC$ with $AB = AC$. Show that $CD < BD$.

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