What reason can be used to prove that the triangles are congruent? A. ASA
B. AAS
C. SAS
D. SSS

C: SAS

Step by step:
The first side is the side that was already established is the same as the other (ab & bc) The angles from point b are congruent because it’s an isosceles triangle so the mid point of the base is the altitude of the triangle and angle bisector of the angle opposite of it. Since it’s an angle bisector both are equal. The third side is the one that they share (bd). Then using SAS you can prove congruency.
Hope that helps :)