nope, we dunno if AB ≅ AC, so we can't quite use SSS for a congruence test.
however, we can do congruence by the smaller triangles of ADB and ADC, we know, since it's given, that BD ≅ CD and since the side AD is the same on both triangles, then we can say that the right-triangles of ADB and ADC have congruent legs where BD ≅ CD and AD ≅ AD, thus by the LL theorem for right-triangles, both triangles are congruent, and thus AB ≅ AC.
LL = Leg Leg, if two legs in two right-triangles are congruent, the triangles are congruent.
