1. Lesson 1-5: Pairs of Angles

2. Lesson 1-5: Pairs of Angles
Adjacent Angles
Definition:
A pair of angles with a shared vertex and common side but do not have overlapping interiors.
Examples:
1 and 2 are adjacent. 3 and 4 are not.
1 and ADC are not adjacent. 4 3
Adjacent Angles( a common side )
Non-Adjacent Angles
Lesson 1-5: Pairs of Angles

3. Lesson 1-5: Pairs of Angles
Complementary Angles
Definition:
A pair of angles whose sum is 90˚
Examples:
Adjacent Angles
( a common side )
Non-Adjacent Angles
Lesson 1-5: Pairs of Angles

4. Lesson 1-5: Pairs of Angles
Supplementary Angles
Definition:
A pair of angles whose sum is 180˚
Examples:
Adjacent supplementary angles are also called “Linear Pair.”
Non-Adjacent Angles
Lesson 1-5: Pairs of Angles

5. Lesson 1-5: Pairs of Angles
Vertical Angles
Definition:
A pair of angles whose sides form opposite rays.
Examples:
Vertical angles are non-adjacent angles formed by intersecting lines.
Lesson 1-5: Pairs of Angles

6. Theorem: Vertical Angles are =~
Given:
The diagram
Prove:
Statements
Reasons 1. 1.
Definition: Linear Pair 2. 2.
Property: Substitution 3. 3.
Property: Subtraction 4. 4.
Definition: Congruence
Lesson 1-5: Pairs of Angles

7. What’s “Important” in Geometry?
4 things to always look for !
360˚
180˚
90˚
Most of the rules (theorems)
and vocabulary of Geometry
are based on these 4 things.
. . . and Congruence
Lesson 1-5: Pairs of Angles

8. Example: If m4 = 67º, find the measures of all other angles.
Step 1: Mark the figure with given info.
Step 2: Write an equation.
67º
Lesson 1-5: Pairs of Angles

9. Lesson 1-5: Pairs of Angles
Example: If m1 = 23 º and m2 = 32 º, find the measures of all other angles.
Answers:
Lesson 1-5: Pairs of Angles

10. Lesson 1-5: Pairs of Angles
Example: If m1 = 44º, m7 = 65º find the measures of all other angles.
Answers:
Lesson 1-5: Pairs of Angles

11. Lesson 1-5: Pairs of Angles
Algebra and Geometry
Common Algebraic Equations used in Geometry:
( ) = ( )
( ) + ( ) = ( )
( ) + ( ) = 90˚
( ) + ( ) = 180˚
If the problem you’re working on has a variable (x),
then consider using one of these equations.
Lesson 1-5: Pairs of Angles