1-5: Exploring Angle Pairs

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Presentation transcript:

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 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 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 Using the diagram, which angles can you conclude are… …congruent? …vertical angles? …adjacent angles? …supplementary angles?

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

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 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 = 3x + 19 and mDBC = 7x – 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?

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