Lesson 1 5 Pairs of Angles Lesson 1

Lesson 1 -5 Pairs of Angles Lesson 1 -5: Pairs of Angles 1

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 2

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 3

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 4

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 5

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

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

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 8

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 9

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

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 11