Question
$\triangle\text{ABC}$ is isosceles with $AB = AC$. Line segment $AD$ bisects $\angle\text{A}$ and meets the base $BC$ in $D$.
Is it true to say that $BD = DC$?

Answer

Now, $\triangle\text{ABD}\cong\triangle\text{ACD}$ therefore by $c.p.c.t.$, $BD = DC$.

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