AMSCO'S Geometry. New York - Rye High School

The Meaning of Locus 611Note that in earlier chapters, we proved two theorems that justify theseresults:• If a point is equidistant from the endpoints of a line segment, then it lieson the perpendicular bisector of the segment.• If a point lies on the perpendicular bisector of a line segment, then it isequidistant from the endpoints of the segment.EXAMPLE 2Construct the locus of points in the interior of an angle equidistant from therays that form the sides of the given angle.ConstructionCorollaries 9.13b and 9.15a together state: A point is equidistant from thesides of an angle if and only if it lies on the bisector of the angle. Therefore,the required locus is the bisector of the angle.1. Make a diagram: ABC is the given angle.AB2. Decide the condition to be satisfied: P is to be equidistant from BA handBC h, the rays that are the sides of ABC. Construct the angle bisector.Use a compass to draw an arc with center B that intersects BA hat R andBC hat S. Then, with the compass open to a convenient radius, draw arcsfrom R and S that intersect in the interior of ABC. Call the intersectionP. PR PS.ACRPBSC3. Through points P and B, draw the ray that is the locus.ARPBSC