ABCD is a quadrilateral such that diagonal AC bisects the angles ∠A and ∠C.

Given: In quadrilateral ABCD, AC bisects the angles ∠A and ∠C.

To prove: AB = AD and CB = CD

Proof:
In ∆">Δ∆ABC and ∆">Δ∆ADC,

∠">∠∠BAC = ∠">∠∠DAC            (Given, AC bisects the angles ∠A)
AC = AC                        (Common side)
∠">∠∠BCA = ∠">∠∠DCA            (Given, AC bisects the angles ∠C)

∴">∴∴ By ASA congruence criteria,
∆">Δ∆ABC ≅">≅≅∆">Δ∆ADC

Hence, AB = AD and CB = CD.     (CPCT)