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1-5: Exploring Angle PairsPowerPoint Presentation

1-5: Exploring Angle Pairs

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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.

- The angles of a linear pair form a straight line.

Finding Missing Angle Measures

- KPL and JPL are a linear pair, mKPL = 2x + 24, and mJPL = 4x + 36.
- What are the measure of KPL and JPL?

ABC and DBC are a linear pair.mABC = 3x + 19 and mDBC = 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 mDAC = 58, what is mDAB?

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