Question

In $\Delta ABCAB=AC$ and D is a point in side BC such that AD bisects angle BAC then AD is perpendicular bisector of side BC
If the above statement is true then mention answer as 1, else mention 0 if false

Answer 1

In $△ABD$ and $△ACD$,
$\angle BAD=\angle CAD$ (Given)
$AD=AD$ (Common)
$AB=AC$ (Given)
Thus, $△ABD\cong △ACD$ (SAS rule)
Hence, $BD=CD$ (By cpct)
$\angle ADB=\angle ADC=x$ (By cpct)
$\angle ADB+\angle ADC=180$
$x+x=180$
$x={90}^{\circ }$
Thus, $\angle ADB=\angle ADC={90}^{\circ }$
Hence, AD is perpendicular bisector of BC