\(ABCD\) is a quadrilateral in which \(AB = BC\) and \(AD = CD\). Show that \(BD\) bisects both the angles \(ABC\) and \(ADC\).
Proof:
Consider \(\triangle ABD\) and \(\triangle CBD\).
\(\triangle ABD \cong \triangle CBD\) [By Congruence rule]
\(\angle 1 = \angle 2\)
\(\angle 3 = \angle 4\)
Thus, \(BD\) bisects both the angles \(ABC\) and \(ADC\).