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1.5 Exploring Angle Pairs 9/20/10

1.5 Exploring Angle Pairs 9/20/10. Types of Angle Pairs Adjacent Angles Vertical Angles Complementary Angles Supplementary Angles. Adjacent Angles. Adjacent angles – two coplanar angles with a common side, a common vertex, and no common interior points. Vertical Angles.

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1.5 Exploring Angle Pairs 9/20/10

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  1. 1.5 Exploring Angle Pairs 9/20/10 • Types of Angle Pairs • Adjacent Angles • Vertical Angles • Complementary Angles • Supplementary Angles

  2. Adjacent Angles • Adjacent angles – two coplanar angles with a common side, a common vertex, and no common interior points.

  3. Vertical Angles • Vertical angles – two angles whose sides are opposite rays.

  4. Complementary Angles • Complementary angles – two angles whose measures have a sum of 90°. • Each angle is called the complement of the other.

  5. Supplementary Angles • Supplementary angles – two angles whose measures have a sum of 180°. • Each angle is called the supplement of the other.

  6. Identifying Angle Pairs • Use the diagram. Is the statement true? Explain. a. are adjacent angles. b. are vertical angles. c. are complementary.

  7. Identifying Angle Pairs • No, they are not adjacent. They have a common side and common vertex, but they also have common interior points. • No, they are not vertical angles. Ray FA and ray FD are opposite rays, but ray FE and ray FB are not. • Yes, they are complementary. 62 + 28 = 90°.

  8. Linear Pairs • A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. • The angles of a linear pair form a straight angle. • Postulate 1.9 Linear Pair Postulate • If two angles form a linear pair, then they are supplementary.

  9. Finding Missing Angle Measures are a linear pair. What are the measures of ?

  10. Finding Missing Angle Measures

  11. Angle Bisector • An angle bisector is a ray that divides an angle into two congruent angles. • Its endpoint is at the angle vertex. • Within the ray, a segment with the same endpoint is also an angle bisector. • The ray or segment bisects the angle.

  12. Using an Angle Bisector to Find Angle Measures • bisects . If , what is

  13. More Practice!!!!! • Classwork – Textbook p. 38 # 7 – 25 odd. • Homework – Textbook p. 38 # 8 – 26 even.

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