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 R AOC then:  m R AOB + m R BOC = m R AOC

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?  R 1 and R 4 are vertical?  R 1 and R 5 are supplementary?  R 3 is a right angle?  R 2 and R 3 are adjacent?  R 1 and R 2 are congruent?