1-4: Measuring Angles. Parts of an Angle An angle is formed by two rays with the same endpoint. The rays are the sides of the angle and the endpoint is.

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Presentation transcript:

1-4: Measuring Angles

Parts of an Angle An angle is formed by two rays with the same endpoint. The rays are the sides of the angle and the endpoint is the vertex of the angle. The interior of an angle is the region containing all points between the sides of the angle. The exterior of an angle is the region containing all points outside the angle.

Naming an Angle You can name an angle by its vertex (  A), a point on each ray and the vertex (  BAC or  CAB), or a number (  1). *Note: When using 3 points to name an angle, the vertex must go in the middle!

Naming Angles What are two other names for  1? What are two other names for  KML?

Measuring Angles One way to measure the size of an angle is in degrees. To say that the measure of  A is 62 , you would write m  A = 62 . Protractor Postulate: Consider OB and point A on one side of OB. Every ray of the form OA can be paired one to one with a real number from 0 to 180.

Types of Angles You can classify angles according to their measures. Symbol for right angle!

Measuring and Classifying Angles What are the measures of  LKN,  JKL, and  JKN? Classify each as acute, right, obtuse, or straight.

Congruent Angles Angles with the same measure are congruent angles. This means that if m  A = m  B, then  A   B (and vice versa). You can mark angles with arcs to show they are congruent.

Using Congruent Angles Synchronized swimmers form angles with their bodies. If m  GHJ = 90 , what is m  KLM? If m  ABC = 49 , what is m  DEF?

 Which angle is congruent to  WBM?

Angle Addition Angle Addition Postulate: If point B is in the interior of  AOC, then m  AOB + m  BOC = m  AOC.

Using the Angle Addition Postulate If m  RQT = 155 , what are m  RQS and m  TQS?

 If m  ABC = 175 , what are m  ABD and m  CBD?