Download 1.6 Notes Angle Pairs

Notes F1: 10-20-15
Homework - Online (Assn. 9-1)
Goals
1) Identify and use special pairs of angles.
2) Write model equations and use them to
find measure of angles.
Notes E1
Goals
1.6 Angle Pairs
Angle Pairs
Note 1
Four Types
*Angle Pairs are referring to angles that are in groups of two.
Four types...
1) Complementary Angles Two angles are complementary if the sum of their
measures is 90
Complementary Angles
Sum is 90
Note 1
1, 2 are complementary angles
Note 2
Model Equation
1 and 2 are complements of each other.
Model Equation
1
MODEL EQUATION
2
m1 + m2 = 90
2) Supplementary Angles Two angles are supplementary if the sum of their
measures is 180
Supplementary Angles
Sum is 180
Note 2
Note 1
Model
1, 2 are supplementary angles
1
Equation
1 and 2 are supplements of each other
2
MODEL EQUATION
m1 + m2 = 180
Common Mistake
****COMMON MISTAKE ALERT****
Not adjacent
Question
*Complementary and Supplementary angles DO NOT HAVE TO BE ADJACENT ANGLES.
Informally
Formally
Diagrams
What are adjacent angles?
Adjacent angles are "next to" each other.
Share a side, have no common interior points.
37
122
53
58
3) Vertical Angles Two angle are Vertical Angles if their sides form opposite rays.
Vertical Angles
Opp rays
The pair of vertical angles are going to be...1, 3; 2, 4
Pair of VA
Across
Congruent
*Angles that are "across from each other"
2
1
*Vertical Angles are congruent
4
MODEL EQUATION
4) Linear Pair
Model
Equation
3
m1 = m3
m2 = m4
Two angles form a Linear Pair if they are supplementary, adjacent angles.
Linear Pair
*Look a lot like supplementary angles
Supp Angles
Adjacent
*Only difference is that they MUST be adjacent.
Supp-Adj
Model
1
2
MODEL EQUATION
m1 + m2 = 180
Equation
ANGLE PAIR MODEL EQUATIONS
Model Equations
Comp Angles
1) Complementary Angles
2) Supp. Angles / Linear Pair
3) Vertical Angles
Equation
Supp/LP
Equation
m1 = m2
Vertical Angles
Equation
m1 + m2 = 180
1
m1 + m2 = 90
1
2
1
2
2