In a triangle, if the angular bisector bisects its opposite side, then the triangle is

By vertical angle bisector theorem

$\frac{AB}{AC}=\frac{BD}{DC}$ $\Rightarrow$ $\frac{AB}{AC}=\frac{BD}{BD}$

$\therefore$ $\frac{AB}{AC}=\frac{1}{1}$ $\Rightarrow$ $AB=AC$

$\Rightarrow$ $\Delta ABC$  is an isosceles