In Figure, diagonal `A C` of a quadrilateral `A B C D` bisects the angles `A` and `C` . Prove that `A B=A D` and `C B=c ddot`

Explanation

Given In a quadrilateral ABCD ,diagonal AC bisects the angle A and C .

To prove AB= AD and CB =CD
Proof in `Delta ADC and Delta ABC `
`angle DAC = angle BAC ` [`because AC "is the bisector of" angle A and angle C]`
`angle DCA = angle BCA `[` because AC " is the bisector of" angle A and angle C`]
and AC= AC [common side ]
`therefore Delta ADC cong Delta ABC` [by ASA congruence rule ]
AD=AB [by CPCT ] and CD =CB [by CPCT]