1. 1 Unit 5: Geometry Pairs of Angles

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

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

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

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

6. Lesson 1-5: Pairs of Angles 6 Theorem: Vertical Angles are = The diagramGiven: Prove: ~ StatementsReasons 1. 2.3.4. 1. Definition: Linear Pair 2. Property: Substitution 3. Property: Subtraction 4. Definition: Congruence

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

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

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

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

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