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Geometric constructions: angle bisector

CCSS.Math:

Video transcript

we're asked to construct an angle bisector for the given angle so this is the angle they're talking about and they want us to make a line that goes right in between that angle that divides that angle into two two angles that have equal measure that have half the measure of the first angle so let's first find two points that are equidistant from this point right over here on each of these rays so to do that so to do that let us let us add let's draw one circle here and I can make this of any radius wherever this intersects with the Rays that's where I'm going to put a point so let's let's say here and here notice both of these points since they're both on this circle are going to be equidistant from this point which is the center of the circle now what I want to do is construct a line construct a line that is equidistant from both of these points and we've done that already when we looked at perpendicular bisectors for lines in this in this construction module so let's do that so let's add there compass and so what I want to do this circle is centered at this point and it has a radius equal to the distance between this point and that point and then I do that again so this circle is centered at this point and has a radius equal to the distance between that point and that point and then the two places where they intersect are equidistant to both of these points they're equidistant to both of these points and so we can now draw our angle bisector just like that and you might say well how do we how do we really know how do we really know that this angle is equal to this angle well there's a couple of ways we can tell we know this distance right over here is equal to this distance right over there we know that this distance over here is equal to this distance over here and both of these triangles share this line so you have essentially if you look at this point at this point at this point that forms a triangle and if you look at this point this point at this point that forms a triangle we know those two triangles are congruent so this angle must be equal to this angle these are the corresponding so they're going to be congruent this is a angle bisector