If ac bisects bad and bcd prove bac=dac

ΔBAC ≅ ΔDAC  by ASA congruency

Step-by-step explanation:

Congruency of any triangle can be proved by either of these four criteria. These include

SSS, SAS, ASA, AAS where S= sides and A= Angles  

In the given figure ΔBAC & ΔDAC

Since the line, AC is a common angular bisector of ∠BAC and ∠DAC

∴ ∠BAC = ∠DAC               ∵ AC is an angular bisector and bisects the ∠BAD into two halves

    ∠BCA=∠DCA                ∵AC is an angular bisector and bisects the  ∠DCB into two halves

AC=AC                                 ∵Common side

∴ ΔBAC ≅ ΔDAC                    ⇒by Angle-Side-Angle (ASA) congruency criterion