Question

ac bisects ∠bcd
reason: given
∠bca≅∠dca
reason: an angle bisector divides an angle into two congruent angles
△abc≅△adc
reason:

Explanation:

Step1: Recall angle - bisector property

An angle bisector divides an angle into two congruent angles. Given that $\overline{AC}$ bisects $\angle BCD$, we have $\angle BCA\cong\angle DCA$.

Step2: Identify congruence postulate

To prove $\triangle ABC\cong\triangle ADC$, we need more information. If we assume that $AC = AC$ (common side) and we have the angle - bisector property $\angle BCA\cong\angle DCA$, and if we also have another pair of corresponding sides or angles equal. For example, if $BC = DC$, then by the Side - Angle - Side (SAS) congruence postulate, $\triangle ABC\cong\triangle ADC$. But if we assume that $\angle BAC\cong\angle DAC$ along with $\angle BCA\cong\angle DCA$ and $AC=AC$, then by the Angle - Side - Angle (ASA) congruence postulate, $\triangle ABC\cong\triangle ADC$.

Let's assume we have enough information such that we can use the ASA (Angle - Side - Angle) congruence postulate.

Answer:

ASA (Angle - Side - Angle) congruence postulate.