Answer:
ASA
Explanation:
You are given 2 equal sets of angles.
<ABD and <ACD (right angles)
<BAD and <CDA (bisected angle)
You can get <ADB = <ADC because every triangle has 180 degrees. You know two of the angles: you can show that the 3 rd set are equal a subtraction postulate.
AD = AD (Reflexive property)
The triangles are congruent by ASA
If AAS is acceptable then it is correct in this case.
AD = AD
The two right angles are equal
The two angles created by the angle bisector are equal.
These three facts give AAS, but please see my comment below.