AMSCO'S Geometry. New York - Rye High School

16 Essentials of Geometry1. By a capital letter that names its vertex.CExample: A2. By a lowercase letter or number placedinside the angle.vertex AsidexsideBExample: x3. By three capital letters, the middle letter naming the vertex and each of theother letters naming a point on a different ray. Example: BAC or CABTSWhen a diagram shows several angles with the same vertex, we avoid confusionby using three letters to name each angle. For example, in the figure, thesmaller angles are RPS and SPT; the larger angle is RPT.PRStraight AnglesDEFINITIONA straight angle is an angle that is the union of opposite rays.B O AThe sides of a straight angle belong to the same straight line. In the figure,OA hand OB hare opposite rays of AB gbecause they have a common endpoint, O,and no other points in common. Thus, AOB is a straight angle because it is theunion of the opposite rays OA hand OB h.An angle divides the points of a plane that are notpoints of the angle into two sets or regions. One regionis called the interior of the angle; the other region iscalled the exterior of the angle. In the figure, A is nota straight angle. M is any point on one side of A and MN is any point on the other side of the angle.PNeither M nor N is the vertex of the angle. Anypoint P on MN between points M and N belongs to the interiorinterior region of the angle. The region consisting of all of anglepoints such as P is called the interior of the angle. All ANexterior of angleother points of the plane, except the points of the angleitself, form the region called the exterior of the angle.The Measure of an AngleTo measure an angle, we must select a unit of measure and know how this unitis to be applied. In geometry, the unit used to measure an angle is usually adegree. The number of degrees in an angle is called its degree measure.The degree measure of a straight angle is 180. A degree is, therefore, the1measure of an angle that is 180 of a straight angle. It is possible to use units otherthan the degree to measure angles. In this book, when we write mHRC 45,we mean that the measure of HRC is 45 degrees.