Transcript Mathn II 1-5 Exploring Angle Pairs

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:
TW  WV ?
PW  WQ?
TWQ is a right angle?
TV bisects PQ?
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?