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1-5: Exploring Angle Pairs

1-5: Exploring Angle Pairs. Types of Angle Pairs. Adjacent angles are two angles with a common side, common vertex, and no common interior points (next to). Vertical angles are two angles whose sides are opposite rays (across from). Types of Angle Pairs, con’t.

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1-5: Exploring Angle Pairs

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  1. 1-5: Exploring Angle Pairs

  2. Types of Angle Pairs • Adjacent angles are two angles with a common side, common vertex, and no common interior points (next to). • Vertical angles are two angles whose sides are opposite rays (across from).

  3. Types of Angle Pairs, con’t • Complementary angles are two angles whose measures have a sum of 90. • Each angle is the complement of the other. • Supplementary angles are two angles whose measures have a sum of 180. • Each angle is the supplement of the other.

  4. Identifying Angle Pairs • Using the diagram, decide whether each statement is true. • BFD and CFD are adjacent angles. • AFB and EFD are vertical angles. • AFE and BFC are complementary. • AFE and CFD are vertical angles. • DFE and BFC are supplementary. • AFB and BFD are adjacent.

  5. Making Conclusions from a Diagram • Using the diagram, which angles can you conclude are… …congruent? …vertical angles? …adjacent angles? …supplementary angles?

  6. Making Conclusions From a Diagram • Using the diagram, can you conclude the following: ? ? TWQ is a right angle? bisects ?

  7. 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 line. Linear Pair Postulate: If two angles form a linear pair, then they are supplementary.

  8. Finding Missing Angle Measures • KPL and JPL are a linear pair, mKPL = 2x + 24, and mJPL = 4x + 36. • What are the measure of KPL and JPL?

  9.  ABC and DBC are a linear pair.mABC = 3x + 19 and mDBC = 7x – 9. What are the measures of ABC and DBC?

  10. Angle Bisectors • An angle bisector is a ray that divides an angle into two congruent angles. • Its endpoint is at the angle vertex.

  11. Using an Angle Bisector • AC bisects DAB. If mDAC = 58, what is mDAB?

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