1. Lesson 2.8 Vertical Angles Objective: After studying this lesson you will be able to recognize opposite rays and vertical angles.

2. A Definition Two collinear rays that have a common endpoint and extend in different directions are called opposite rays. B C

3. Are all pairs of rays called opposite rays? OM J K A B C D Key questions: Are they on the same line? Do the rays share the same endpoint?

4. Vertical Angles Whenever two lines intersect, two pairs of vertical angles are formed. 1 2 3 4 DefinitionTwo angles are vertical angles if the rays forming the sides of one and the rays forming the sides of the other are opposite rays

5. Are angle 3 and angle 2 vertical angles? How do vertical angles compare in size? 1 2 3 4 Theorem 18 Vertical angles are congruent 92Find the missing angles

6. Diagram as shown Given: Prove: Statements Reasons 5 7 6

7. Statements Reasons Given: Prove: 1 2 3

8. Statements Reasons Given: Prove: 1 2 O M J H K

9. Given: Find: 4 5

10. Lesson 2.8 Worksheet Homework Summary… Explain what opposite rays are and how they relate to vertical angles?