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Understanding Angles: Definitions, Naming, and Classification

This lesson focuses on the basics of angles, including their formation by two non-collinear rays with a common endpoint known as the vertex. Learn how to accurately name angles using various methods, such as three points, one point, and numerical identifiers. The lesson also covers angle classification (acute, obtuse, right, and straight) and introduces congruent angles. Key concepts discussed include the Angle Addition Postulate and practical examples for better understanding.

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Understanding Angles: Definitions, Naming, and Classification

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  1. Angle Measure Sec: 1.4

  2. Angles • Are formed By two non-collinear rays. • They have a common endpoint. • The two rays are called sides of an angle. • The common endpoint is the vertex. Side B Vertex A C Side

  3. There are three ways to name an angle(1) Using 3 points, (2) Using 1 point (3) Using a number – next slide A C B Lesson 1-4: Angles

  4. Naming an Angle - continued Using a number: A B 2 C Lesson 1-4: Angles

  5. Example 1 • Name the following angle. B A 4 C

  6. Example 2Name the different angles Lesson 1-4: Angles

  7. Example 3Name the angles • K is the vertex of more than one angle. Therefore, there is NO in this diagram. Lesson 1-4: Angles

  8. Notes - Angle and Points • Angles can have points in the interior, in the exterior or on the angle. E A D B C Points A, B and C are on the angle. D is in the interior and E is in the exterior. B is the vertex. Lesson 1-4: Angles

  9. Example 4 Name all angles with B as a vertex. 2. Name the sides of angle 5. 3. Write another name for angle 6.

  10. Classifying Angles: D A B C

  11. Example 5 Classify each angle as right, obtuse, acute or straight. 1. Angle TYV 2. Angle WYT 3. Angle TYU 4. angleTYX

  12. Congruent angles • Two angles with the same angle measure are said to be congruent. Example:

  13. Angle Addition Postulate Postulate: The sum of the two smaller angles will always equal the measure of the larger angle. Complete: m  ____ + m ____ = m  _____ MRK KRW MRW Lesson 1-4: Angles

  14. Example 6 m1 + m2 = Therefore, mADC = Lesson 1-4: Angles

  15. Example 7: Angle Addition K is interior to MRW, m  MRK = (3x), m KRW = (x + 6) and mMRW = 90º. Find mMRK. Lesson 1-4: Angles

  16. Example 8:Angle Addition K is interior to MRW, m  MRK = (2x + 10), m KRW = (4x - 3) and mMRW = 145º. Find mMRK and m KRW. Lesson 1-4: Angles

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