ANSWER
The SAS congruence postulate
Step-by-step explanation
We want to find the reason why triangle BAD and CAD are congruent.
From the question, we are given that sides AB and AC are congruent since triangle ABC is an isosceles triangle.
It has also been shown that there is a pair of congruent angles and a side that is common to both triangles.
This means that there are two sets of sides and one set of angles that are congruent in the triangles.
Hence, according to the SAS (Side-Angle-Side) congruence postulate, the two triangles, BAD and CAD, are congruent.