ABCD is a quadrilateral such that diagonal AC bisects the angles A and C. Prove that AB = AD and CB = CD.
Given: ABCD is quadrilateral
AC bisects A and C
To prove: AB = AD, CB = CD
In ABC and ADC
BAC = DAC ( AC bisects A)
AC = AC (common)
BAC = DCA (AC bisects C)
ABC ADC (by ASA criterion)
AB = AD (by CPCT)
BC = CD. (by CPCT)
Hence proved.