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Understanding and Identifying Angle Pairs in Geometry

This guide explores various types of angle pairs, including adjacent, vertical, complementary, and supplementary angles. It discusses how to identify these angle pairs using diagrams and provides examples and exercises to apply the concepts. The content also covers linear pairs and angle bisectors, explaining the relationships between angles and helping students determine missing angle measures. Ideal for students seeking to strengthen their understanding of angle relationships in geometry.

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Understanding and Identifying Angle Pairs in Geometry

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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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