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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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Types of 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
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.


Identifying angle pairs
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.


Making conclusions from a diagram
Making Conclusions from a Diagram

  • Using the diagram, which angles can you conclude are…

    …congruent?

    …vertical angles?

    …adjacent angles?

    …supplementary angles?


Making conclusions from a diagram1
Making Conclusions From a Diagram

  • Using the diagram, can you conclude the following:

    ?

    ?

    TWQ is a right angle?

    bisects ?


Linear pairs
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.


Finding missing angle measures
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?


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


Angle bisectors
Angle Bisectors

  • An angle bisector is a ray that divides an angle into two congruent angles.

  • Its endpoint is at the angle vertex.


Using an angle bisector
Using an Angle Bisector

  • AC bisects DAB. If mDAC = 58, what is mDAB?


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