Question

ac bisects ∠bad
reason: given
∠bac≅∠dac
reason: select reason
ab≅ad
reason: select reason
ac≅ac
reason: select reason
△abc≅△adc
reason: select reason

Explanation:

Step1: Definition of angle - bisector

If a ray bisects an angle, it divides the angle into two congruent angles. Since $\overline{AC}$ bisects $\angle BAD$, then $\angle BAC\cong\angle DAC$.

Step2: Given side - equality

If $\overline{AB}\cong\overline{AD}$ is given in the problem - context (not shown in the "Given" statement in the first box but could be an additional given), the reason for $\overline{AB}\cong\overline{AD}$ is "Given".

Step3: Reflexive property of congruence

For any segment $\overline{AC}$, $\overline{AC}\cong\overline{AC}$ by the reflexive property of congruence which states that any geometric figure is congruent to itself.

Step4: Side - Angle - Side (SAS) congruence criterion

Since we have $\angle BAC\cong\angle DAC$, $\overline{AB}\cong\overline{AD}$, and $\overline{AC}\cong\overline{AC}$, by the Side - Angle - Side (SAS) congruence criterion, $\triangle ABC\cong\triangle ADC$.

Answer:

For $\angle BAC\cong\angle DAC$: Definition of angle - bisector; For $\overline{AB}\cong\overline{AD}$: Given (if provided as such); For $\overline{AC}\cong\overline{AC}$: Reflexive property of congruence; For $\triangle ABC\cong\triangle ADC$: Side - Angle - Side (SAS) congruence criterion.