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1-5: Exploring Angle Pairs

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# 1-5: Exploring Angle Pairs - PowerPoint PPT Presentation

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

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. 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?