what i want to do first is just show you what the angle bisector theorem is and then we'll actually prove it for ourselves so i just have an arbitrary triangle right over here triangle A, B, C and what im going to do is im going to draw an angle bisector for this angle up here we could have done it with any of the three angles but i'll just do this one it'll make our proof a little bit easier so im just gonna bisect this angle, angle ABC so lets just say that that's the angle bisector of angle ABC