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Understanding Angle Measurements and Classifications: Lesson 2 of 2

In this second lesson on measuring segments and angles, students delve into angle vocabulary, learning to identify and classify angles based on their measurements. Angles are defined with specific terminology, including acute, right, obtuse, and straight angles. The lesson covers the naming conventions for angles, congruency, and the Angle Addition Postulate, enhancing comprehension of angle relationships. Practice problems and a homework assignment reinforce these concepts, preparing students for further geometric studies.

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Understanding Angle Measurements and Classifications: Lesson 2 of 2

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  1. Measuring Segments and Angles, Lesson 2 of 2 During today’s lesson, you will find the measures of angles. .

  2. ANGLE VOCABULARY T 1 B Q TBQ has sides BT and BQ and vertex B An angle () is formed by two rays with the same endpoint. The rays are the sides of the angles and the endpoint is the vertex.

  3. T 1 B Q Angles can be named in 3 different ways: 1. Using 3 points: TBQ or QBT 2. Using the vertex: B 3. Using a number inside the angle: 1 ALERT! When the vertex is shared, you cannot use it to name an angle.

  4. An acute angle has a measure between 0° and 90°. A right angle has a measure a measure of exactly 90°. An obtuse angle has a measure a measure between 90° and 180°.

  5. A straight angle has a measure of exactly 180°. Congruent angles are two angles with the same measure.

  6. Notation for congruent angles: Use ABC DEF when referring to the actual angles. Use mABC = mDEF when referring to the measure of the angles.

  7. A D 30° 30° A D B E C F E B F C Actual angles Use ABC DEF Measures (degrees) Use mABC = mDEF

  8. B A O C B A O C Angle Addition Postulate If point B is in the interior of AOC, then mAOB + mBOC = mAOC Also, if AOC is a straight angle, then mAOB + mBOC =180°

  9. T W R S EX. #2 What is mTSW if the mRST = 50 and mRSW = 125? Angle Addition Postulate mRST + mTSW = m RSW Substitute: 50 + mTSW = 125 Solve: mTSW = 75

  10. Final Checks for Understanding • Name four ways by which we classify angles based upon their degree measure. • Use the diagram below to answer the following questions: a. Is DEF  FEG? b. Is Is DEF  FEG? c. Are DEF and FEH adjacent? F G 45 45 D E H

  11. HOMEWORK ASSIGNMENT PAGES 30-32: 16-28, 47-48, 59-61,65-66,75-76 Show work when necessary!

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