let me call it point D the angle bisector theorem tells us that the ratio between the size that aren't this bisector so when i put this angle bisector here it created two smaller triangles out of that large one the angle bisector theorem tells us that the ratios between the other sides of these two triangles that we now created are going to be the same so it tells us that the ratio of AB to AD is going to be equal to the ratio of BC to - you could say to CD,so the ratio of - i'll color code it - the ratio of - that, which is this, to this, to this is going to be equal to the ratio of this -which is that- to this right over here to CD - which is that over here so it kind of - once you see the ratio of that to that is going to be the same as the ratio of that to that so that's kind of a cool result but you cant just accept it on -on- faith because its a cool result! you want to prove it to ourselves and so you could imagine right over here we have some ratio set up so we're gonna prove it using similar triangles and unfortunate for us these two triangles right here - aren't necessarily similar! we cant really we know that these two angles are congruent to each other but we dont know whether this angle is equal to that angle or that we dont know we cant make any statements like that so in order to actually set up this type of a statement we'll have to construct maybe another triangle! that will be similar to one of these right over here and one way to do it-