AC bisects angle DAB, which tells us that angle DAC and angle CAB are the same measure (in this case, each is 106/2 = 53 degrees).
Because angle DAC = angle CAB, this forms the second "A" of "AAS". The first "A" is due to angle ABC = angle ADC.
The "S" refers to AC = AC by the reflexive property.
"Angle-Angle-Side" shortens to "AAS". Be sure not to mix it up with ASA which is a similar theorem. In the case of AAS, the side is not between the angles mentioned. If we knew that AB = AD, then we could use ASA.
