check the picture below.
recall, AB = AC, and AR is an angle bisector to the vertex A, so A gets split into two equal angles, so those angles are twins.
now, the segment AR is part of triangle ABR and is also part of the triange ACR, however, is being shared by both, and therefore, is the same length on each triangle.
so you have a Side, in green, an Angle, from the twins, and another Side, being shared by both, Side Angle Side, SAS.
