## Constructing an Angle Bisector

the key points to an angle bisector is that it does almost lost dirt is that it does a couple things the first thing is it bisects the angle creating two congruent angles so if I have an angle that's in blue here and the red ray is my angle bisector then it has created two congruent angles so notice that this red is a rape so that's another key thing now it also could be a line segment if you're talking about something in a nice ah sleaze triangle perhaps perhaps so we could say or a line segment and every point along this bisector is the same distance from the two rays that make up the sides but how do we measure distance well the shortest distance from a point on this ray to a ray that forms the angle is along a perpendicular so if you're to construct the perpendicular from the angle bisector to a side and if you did that down here then you would say that these two segments are congruent so that's the key parts to an angle bisector is that bisects the angle creating two congruent angles that it is a liner or it is a ray or a line segment and that every point on this ray is the same distance measured along the perpendicular from the Rays that make up your angle but how do we actually construct them well to do that let's grab our compass and our straightedge and head over to this angle right here so we know that we're going to create a ray that creates two congruent angles so the first thing you're gonna do is you're gonna swing an arc just like if you were duplicating an angle so from the vertex I'm going to swing an arc so that I create two points of intersection now I want to create a point out here that is the same distance from these two points of intersection so if you want to you can change your company but you don't have to for the sake of argument I will and you're going to swing an arc from each of these end points so there's one arc from this intersection here's another point of intersection that I'm going to swing an arc from now this point right here is the same distance from both of these endpoints so I'm going to connect this point of intersection with my vertex thereby creating my angle bisector so I'm going to draw this connect my vertex and that point of intersection and what we've created are two congruent angles then when they sum you get the angle that you started with