Geo1.5 and 2.6.notebook 1 August 31, 2017 Warm Up: What is the measure of if ?
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Warm Up: What is the measure of if ?
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Learning Goal: Today I will learn about angle pairs and the relationship between vertical angles.
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Success Criteria: I am able to identify angle pairs and apply their properties to solve.
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1.5 Exploring Angle Pairs
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a pair of coplanar angles that have a common side, a common vertex, and no common interior points.
*Adjacent Angles
andand
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Draw angle DEF adjacent to angle AEF.
Common side: Common vertex:
*Adjacent Angles
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2 angles whose sides form 2 pairs of opposite rays.*Vertical Angles
andand
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Draw AB and CD intersecting at point E.
Vertical angles are:
*Vertical Angles
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2 angles whose measures have a sum of 90o. Each angle is called the complement of the other.
*Complementary Angles
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Complementary angles are:
Angles 1 and 2 are also __________ angles.
B
A
*Complementary Angles
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2 angles whose measures have a sum of 180o. Each angle is called the supplement of the other.
*Supplementary Angles
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Supplementary angles are:They are also:
*Supplementary Angles
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Example
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a pair of adjacent angles whose non common sides are opposite rays (line).
Angles 1 and 2 are a linear pair.
1 2
*Linear Pair
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Angle DBC and angle DBA are a linear pair.Non common sides:Common sides:
*Linear Pair
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If 2 angles form a linear pair then they are supplementary.
*19 Linear Pair Postulate
If
find
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2.6 Proving Angles Congruent
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Vertical angles are congruent.*21 Vertical Angle Theorem
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21 3
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Which angles are congruent?Which angle pairs are vertical angles?Which angle pairs are adjacent angles?Which angle pairs are adjacent supplementary angles?
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Using the TheoremsFind the value of the variable(s).
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Closure: Today I learned about angle pairs and their relationships.
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