\(ABCD\) is a quadrilateral such that diagonal \(AC\) bisects the angles \(A\) and \(C\). Prove that \(AB = AD\) and \(CB = CD\).
Proof:
In \(\triangle ADC\) and \(\triangle ABC\), we have:
\(\angle DAC = \angle \) [\(AC\) is the bisector of \(\angle A\)]
\(\angle DCA = \angle \) [\(AC\) is the bisector of \(\angle C\)]
\(AC = AC\) [Common side]
Then, by congruence rule]\(\triangle ADC \cong \triangle ABC\)
So, \(AD = AB\) [By CPCT]
Also, \(CD = CB\) [By CPCT]
Hence, we proved.