Honors Geometry Companion Book, Volume 1

1.1.3 Measuring and Constructing Angles Key Objectives • Name and classify angles. • Measure and construct angles and angle bisectors. Key Terms • An angle is a figure formed by two rays, or sides, with a common endpoint called the vertex . • The set of all points between the sides of the angle is the interior of an angle . • The exterior of an angle is the set of all points outside the angle. • The measure of an angle is usually given in degrees.

• Since there are 360° in a circle, one degree is 1/360 of a circle. • An acute angle measures greater than 0° and less than 90°. • A right angle measures 90°. • An obtuse angle measures greater than 90° and less than 180°. • A straight angle is formed by two opposite rays and measures 180°. • Congruent angles are angles that have the same measure. • An angle bisector is a ray that divides an angle into two congruent angles. Theorems, Postulates, Corollaries, and Properties • Protractor Postulate Given  AB and a point O on 

AB , all rays that can be drawn from O can be put into

a one-to-one correspondence with the real numbers from 0 to 180. • Angle Addition Postulate If S is in the interior of ∠ PQR , then m ∠ PQS + m ∠ SQR = m ∠ PQR . Example 1 Naming Angles An angle is a figure formed when two rays meet at a common endpoint. The rays are called the angle’s sides, and the common endpoint is called the angle’s vertex. There are three ways to name an angle. If an angle’s vertex is not a point on any other angle, then the angle can be named using only its vertex. For example, if A is the vertex of an angle and A is not a point on any other angle (i.e., A is not a vertex of another angle and A is not on the side of another angle), then the angle can be named ∠ A , where ∠ is the symbol for angle. The second method for naming an angle is with a number. For example, if 1 is used to label an angle in a figure, then the angle can be named ∠ 1. The third method for naming an angle is explained in the example below.


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