AMSCO'S Geometry. New York - Rye High School

ABB A OEvery point on a line divides the line intotwo opposite sets of points called half-lines. Ahalf-line half-linehalf-line consists of the set of all points on oneside of the point of division.The point of divisionitself does not belong to the half-line. In theM P A Bfigure, point P divides MB into two half-lines.DEFINITIONA ray consists of a point on a line and all points on one side of the point.This definition tells us that a ray is a set of all the points in a half-line andthe dividing point. The dividing point is called the endpoint of the ray.A ray is named by placing an arrow that points to the right over two capitalletters. The first letter must name the endpoint of the ray. The second letter maybe the name of any other point on the ray. The figure shows ray AB, whichstarts at endpoint A, contains point B, and extends indefinitely in one direction.Ray AB is written as AB h .Note in the figure that the ray whose endpoint is O may be named OA horOB h. However, it may not be named AB hsince the first capital letter in the nameof a ray must represent its endpoint.A point on a line creates two different rays, each withthe same endpoint. In the figure, AB h and AC hray rayare oppositerays because points A, B, and C are collinear and C A Bpoints B and C are not on the same side of point A, butare on opposite sides of point A.g Rays and Angles 15DEFINITIONOpposite rays are two rays of the same line with a common endpoint and noother point in common.AnglesDEFINITIONAn angle is a set of points that is the union of two rays having the same endpoint.In the figure, AB hand AC h, which form an angle,are called the sides of the angle. The endpoint ofeach ray, A, is called the vertex of the angle.The symbolfor angle is .An angle, such as the one illustrated, may benamed in any of the following ways:vertex AsidexsideCB