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Understanding Angles: Naming, Measuring & Classifying

Learn about angles, their parts, naming conventions, measurement in degrees, types, congruence, and angle addition postulate with practical examples.

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Understanding Angles: Naming, Measuring & Classifying

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  1. 1-4: Measuring Angles

  2. 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.

  3. 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!

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

  5. 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.

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

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

  8. 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.

  9. 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?

  10.  Which angle is congruent to WBM?

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

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

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

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