Question

In $△ABC,$ the bisector $AD$ of $\angle A$ is perpendicular to side $BC$.Show that $AB=AC$ and $△ABC$ is isosceles.

Answer 1

In $△ABD$ and $△ACD,$

$\angle BAD=\angle CAD$(given)

$AD=AD$(common)

$\angle ADB=\angle ADC={90}^{\circ }$(given)

So,$△ABD\cong △ACD$ by ASA rule

So,$AB=AC$ by CPCT

$\therefore △ABC$ is isosceles triangle.