1-5: Exploring Angle Pairs. Types of Angle Pairs Adjacent Angles Vertical Angles Complementary Angles Supplementary Angles Two coplanar angles with a:

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Presentation transcript:

1-5: Exploring Angle Pairs

Types of Angle Pairs Adjacent Angles Vertical Angles Complementary Angles Supplementary Angles Two coplanar angles with a: _______________, ________________, _______________________________ Two angles whose sides are __________ ______ Two angles whose measures have a sum of _______ common sidecommon vertex no common interior points oppositerays

Example 1: Use the diagram below. Is each statement true? Explain. a. and are adjacent angles. b. and are vertical angles. c. and are supplementary. Yes, they have a common side No, they don’t share two pairs of opposite rays Yes, the sum of the angles is 180°

Assumptions About Angles Assumptions you can make: 1.Angles are adjacent 2.Angles are adjacent and supplementary 3.Angles are vertical angles Assumptions you can’t make: 1.Angles or segments are congruent 2.An angle is a right angle 3.Angles are complementary

Postulate 1-9: Linear Pair Postulate A Linear Pair of angles are angles that are both supplementary and adjacent. Ex 2 What are the measures of and ?

Theorem 2-1: Vertical Angle Theorem Vertical angles are congruent and Example 3: What is the value of x? What are the angle measures?

Angle Bisector A ________ which divides an angle into ______ _______________ angles. ray two congruent is an angle bisector. Example 4: bisects. If, what is ?

Homework: p. 38 # 7-23, 27-32