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CHAPTER 1: Tools of Geometry

CHAPTER 1: Tools of Geometry. Section 1-6: Measuring Angles. Objectives. To find the measures of angles. To identify special pairs of angles. Vocabulary. Angle Acute Angle Right Angle Obtuse Angle Straight Angle Congruent Angles Vertical Angles Adjacent Angles Complementary Angles

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CHAPTER 1: Tools of Geometry

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  1. CHAPTER 1:Tools of Geometry Section 1-6: Measuring Angles

  2. Objectives • To find the measures of angles. • To identify special pairs of angles.

  3. Vocabulary • Angle • Acute Angle • Right Angle • Obtuse Angle • Straight Angle • Congruent Angles • Vertical Angles • Adjacent Angles • Complementary Angles • Supplementary Angles

  4. Angle • An angle is formed by two rays with the same endpoint. • The rays are the “sides” of the angle. • The common endpoint is the “vertex.”

  5. Ways to name an angle: • Using only the vertex. • However, we can only do this if there is only one angle with that vertex. • Using three points. • When we do this, the vertex must be listed in the middle. • Using the assigned number.

  6. Postulate 1-7:“The Protractor Postulate”

  7. Classifying Angles • Acute Angle- an angle less than 90 degrees. • Right Angle- an angle that is exactly 90 degrees. • Obtuse Angle- an angle with a measure greater than 90 degrees but less that 180 degrees. • Straight Angle- an angle that is exactly 180 degrees.

  8. Congruent Angles • Angles with the same measure are congruent angles.

  9. Postulate 1-8:“The Angle Addition Postulate” • If point B is in the interior of RAOC then: • mRAOB + mRBOC = mRAOC

  10. Vertical Angles • Vertical angles are two angles whose sides are opposite rays.

  11. Adjacent Angles • Adjacent angles are two coplanar angles with a common side, common vertex, but no common interior points.

  12. Complementary Angles • Complementary angles are two angles whose measures have a sum of 90 degrees. • Each angle is called the “compliment” of the other.

  13. Supplementary Angles • Supplementary angles are two angles whose measures have a sum of 180 degrees. • Each angle is called the “supplement” of the other.

  14. Identifying Angle Pairs • Identify the pairs of numbered angles that are related as follows: • Complementary • Supplementary • Vertical • Adjacent

  15. Making Conclusions from Diagrams • We can always conclude the following: • Adjacent angles • Adjacent supplementary angles • Vertical angles • We cannot assume unless we are told: • Angles (or segments) are congruent • An angle is a right angle • Lines are parallel • Lines are perpendicular

  16. Making Conclusions: True or False? • R1 and R4 are vertical? • R1 and R5 are supplementary? • R3 is a right angle? • R2 and R3 are adjacent? • R1 and R2 are congruent?

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